MIME-Version: 1.0 Content-Type: multipart/related; boundary="----=_NextPart_01C980C1.3B253F30" This document is a Web archive file. If you are seeing this message, this means your browser or editor doesn't support Web archive files. For more information on the Web archive format, go to http://officeupdate.microsoft.com/office/webarchive.htm ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function

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------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/master06.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAAD1gAAAAUALQAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwC7wLpAwMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAMAAAAQAkhAPAAAAAAAAAA 7wLpA/////8IAAAA+gIAAAAAAAAAAAAABAAAAC0BAgAEAAAALQEAAAQAAAAnAf//HAAAAPsC1P8A AAAAAACQAQAAAAAAQAAAQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAEAAAALQEDAAQA AAAuARgABAAAAAIBAQAFAAAACQIAAAACLQAAADIKOQDwABkAAABUaGUgRXhwb25lbnRpYWwgRnVu Y3Rpb25zABsAGAAZAAwAHgAWABkAGQAYABkAGAAMAAsAGAAKAAwAHAAYABkAFgAMAAoAGQAYABYA BAAAAC4BAAAcAAAA+wIQAAcAAAAAALwCAAAAAAECAiJTeXN0ZW0AAAAAAAAYAAAAMJ4TAAEAAADk BAAAAAAAAAQAAAAtAQQABAAAAPABAwADAAAAAAA= ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0001.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
The Exponential Functions
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0042.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
Recall the special rul= es for exponents:
b0 = =3D 1        = ;            &n= bsp;         b–K = =3D =
b  =3D (Ö b )        = ;            &n= bsp;   b      =3D (       )
K
N
K
N
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>K&#= 13;
1<= /div>
K
N
 Ö b
1
The Exponential Functions
K
N
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0132.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
Recall the special rul= es for exponents:
b0 = =3D 1        = ;            &n= bsp;         b–K = =3D =
b  =3D (Ö b )        = ;            &n= bsp;   b      =3D (       )
K
N
K
N
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>K&#= 13;
1<= /div>
K
N
 Ö b
1
Example A:
8= 0 =3D 1        = ;            &n= bsp;        
The Exponential Functions
K
N
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0133.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
Recall the special rul= es for exponents:
b0 = =3D 1        = ;            &n= bsp;         b–K = =3D =
b  =3D (Ö b )        = ;            &n= bsp;   b      =3D (       )
K
N
K
N
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>K&#= 13;
1<= /div>
K
N
 Ö b
1
Example A:
8= 0 =3D 1        = ;            &n= bsp;         8   =3D       =3D=
82
1
64
1
The Exponential Functions
K
N
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0134.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
Recall the special rul= es for exponents:
b0 = =3D 1        = ;            &n= bsp;         b–K = =3D =
b  =3D (Ö b )        = ;            &n= bsp;   b      =3D (       )
K
N
K
N
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>K&#= 13;
1<= /div>
K
N
 Ö b
1
Example A:
8= 0 =3D 1        = ;            &n= bsp;         8   =3D       =3D=
8  =3D (Ö 8 )
3
2
82
1
64
1
The Exponential Functions
K
N
3
2
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0135.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
Recall the special rul= es for exponents:
b0 = =3D 1        = ;            &n= bsp;         b–K = =3D =
b  =3D (Ö b )        = ;            &n= bsp;   b      =3D (       )
K
N
K
N
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>K&#= 13;
1<= /div>
K
N
 Ö b
1
Example A:
8= 0 =3D 1        = ;            &n= bsp;         8   =3D       =3D=
8  =3D (Ö 8 ) =3D 4        = ;    
3
2
82
1
64
1
The Exponential Functions
K
N
3
2
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0136.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
Recall the special rul= es for exponents:
b0 = =3D 1        = ;            &n= bsp;         b–K = =3D =
b  =3D (Ö b )        = ;            &n= bsp;   b      =3D (       )
K
N
K
N
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>K&#= 13;
1<= /div>
K
N
 Ö b
1
Example A:
8= 0 =3D 1        = ;            &n= bsp;         8   =3D       =3D=
8  =3D (Ö 8 ) =3D 4        = ;          8    =3D (      ) =3D
3
2
82
1
3
2
 Ö 8
1
64
1
The Exponential Functions
K
N
3
2
3
2
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0137.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
Recall the special rul= es for exponents:
b0 = =3D 1        = ;            &n= bsp;         b–K = =3D =
b  =3D (Ö b )        = ;            &n= bsp;   b      =3D (       )
K
N
K
N
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>K&#= 13;
1<= /div>
K
N
 Ö b
1
Example A:
8= 0 =3D 1        = ;            &n= bsp;         8   =3D       =3D=
8  =3D (Ö 8 ) =3D 4        = ;          8    =3D (      ) =3D 1/4=
3
2
82
1
3
2
 Ö 8
1
64
1
The Exponential Functions
K
N
3
2
3
2
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0138.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
Recall the special rul= es for exponents:
b0 = =3D 1        = ;            &n= bsp;         b–K = =3D =
b  =3D (Ö b )        = ;            &n= bsp;   b      =3D (       )
K
N
K
N
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>K&#= 13;
1<= /div>
K
N
 Ö b
1
Example A:
8= 0 =3D 1        = ;            &n= bsp;         8   =3D       =3D=
8  =3D (Ö 8 ) =3D 4        = ;          8    =3D (      ) =3D 1/4=
3
2
82
1
3
2
 Ö 8
1
64
1
The Exponential Functions
K
N
3
2
3
2
Dec= imal exponents are well defined since decimals may be represented reduced fractions.
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0139.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
Recall the special rul= es for exponents:
b0 = =3D 1        = ;            &n= bsp;         b–K = =3D =
b  =3D (Ö b )        = ;            &n= bsp;   b      =3D (       )
K
N
K
N
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>K&#= 13;
1<= /div>
K
N
 Ö b
1
Example A:
8= 0 =3D 1        = ;            &n= bsp;         8   =3D       =3D=
8  =3D (Ö 8 ) =3D 4        = ;          8    =3D (      ) =3D 1/4=
3
2
82
1
3
2
 Ö 8
1
64
1
The Exponential Functions
K
N
3
2
3
2
Dec= imal exponents are well defined since decimals may be represented reduced fractions.
Example B: <= /span>
101.22 =
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0140.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
Recall the special rul= es for exponents:
b0 = =3D 1        = ;            &n= bsp;         b–K = =3D =
b  =3D (Ö b )        = ;            &n= bsp;   b      =3D (       )
K
N
K
N
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>K&#= 13;
1<= /div>
K
N
 Ö b
1
Example A:
8= 0 =3D 1        = ;            &n= bsp;         8   =3D       =3D=
8  =3D (Ö 8 ) =3D 4        = ;          8    =3D (      ) =3D 1/4=
3
2
82
1
3
2
 Ö 8
1
64
1
The Exponential Functions
K
N
3
2
3
2
Dec= imal exponents are well defined since decimals may be represented reduced fractions.
Example B: <= /span>
101.22 = =3D 10   
61<= /div>
50<= /div>
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0141.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
Recall the special rul= es for exponents:
b0 = =3D 1        = ;            &n= bsp;         b–K = =3D =
b  =3D (Ö b )        = ;            &n= bsp;   b      =3D (       )
K
N
K
N
b<= span lang=3DEN-US style=3D'font-size:89%;position:relative;top:-.45em;mso-text-= raise: 30%;mso-fareast-language:ZH-CN'>K&#= 13;
1<= /div>
K
N
 Ö b
1
Example A:
8= 0 =3D 1        = ;            &n= bsp;         8   =3D       =3D=
8  =3D (Ö 8 ) =3D 4        = ;          8    =3D (      ) =3D 1/4=
3
2
82
1
3
2
 Ö 8
1
64
1
The Exponential Functions
K
N
3
2
3
2
Dec= imal exponents are well defined since decimals may be represented reduced fractions.
Example B: <= /span>
101.22 = =3D 10    =3D ( = Ö10 )   » 16.59586….
61<= /div>
50<= /div>
50
61<= /div>
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R0lGODlhIQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAf AAEAgAAAAAAAAAIFjI+pewUAOw== ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0141_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAW AAEAgAAAAAAAAAIEjI+pUQA7 ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0141_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhIQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAg AAEAgAAAAAAAAAIFjI+piwUAOw== ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0141_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhGQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAX 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file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0141_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAS AAEAgAAAAAAAAAIEjI95BQA7 ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0141_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAS AAEAgAAAAAAAAAIEjI95BQA7 ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0141_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAEAgAAAAAAAAAIEjI95BQA7 ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0141_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhEwACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAAAS AAEAgAAAAAAAAAIEjI95BQA7 ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0141_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhHQACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAb AAEAgAAAAAAAAAIEjI+pWgA7 ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0083.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
For real-number-exponent,= we approximate the real number with fractions and use the fractional = powers to approximate the real-number power.
The Exponential Functions
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0142.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
For real-number-exponent,= we approximate the real number with fractions and use the fractional = powers to approximate the real-number power.
10p
<= span lang=3DEN-US style=3D'color:#003300;mso-fareast-language:ZH-CN;mso-special= -format: lastCR;display:none'>
p»3.14159..
Example C:
The Exponential Functions
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0142_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh8QFcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADw AVsAgAAAAAAAAAL/jI+py+0Po5y02ouz3rz7D4biSJbmiabqyrbuCyPATNf2jef6zve+HfgJh7sg 8YgsJpdMgLEJjSKf0qr16jxgt1watXv8gqXicbNsTvvQ6vZV5o7/2PIavd6743X6vbnvF5gDJ+gH GHdY6KQ4xyiX6GioFflIuWjJhzmo+ceJSegJBqk2Gli6dxq6phoJyoqVKvo6E1s5a1V7Szapi2uZ izgL3HtJjOdqzDT8druc5tycfMwrrfwb/QotXP1IzT11vZ39DU5O6m0upB21Ljuerg7/hy7P036G zXoful+PXK+EUj9Y4gAGNAiLHsIbA8u907cwU0RcCifSCvdQVcNP/xar/OtYzNFGjwVBhjSZ5GPH kUNYsisJ0iU3lRZlroLpyaYincloTuR5EGLGmCjPVKyJUahSk0CJ+YzYdBNOTlFRFVV29GdSjVO1 Xk2ZFepWfl3Ffp0SdmFVhvm4Fl0rLC1CuHbakn17Fq2BvHS92M15ta9GuQYFn7y7lGheIk/VjgU8 dOVixoQBGjYcFDHTyS0r+3tMtaxjznM8y7v8NzRe0mtMw0MtWmBg1q33noUdWTVKzFRdp8OdGPJu 2nl8mwPuNjhS4kWMk0OuObpk5nycf4MuPPlm6oOszwStiTcO8WPI//JeDbtu7Yq5M0QvTX342IXd j4ffEzzH3F7t2//Bb4x8+ynXn3+0xIBgggouyGCDDj4IYWNz6UdhK7MZ6AWATlVoIX9mYZiFbV8J yCEj5nVxYisa9kKibB6OBqKE9bn4Io3bxbiiLi12SOCHGMpoWYkm0hckiCGm6A6PPQr5mpFH8sVk IUgethyOIl6oJHvZtfdjjqkJMiWV861mZZhb7CgSkZ8ZCeSaWUq3HpcGtnlalGCqWSebXuLpRphT mkmSnleSmSafdxI65541HvPlgDd2OehwNmoZ53RlQjkpnGNKeultdppi6HFO0tlkplueWiWkgDJj aqWuFphopI8OGaohWKqK6Zuobjqrf6T+9qmtixbZ6YjBWjWsm7iketoqr5r6GOuqvjTr6LMwLmss tcfWIS0U3U4jq5w7NbptfKMquiSyyY6LqK/oUnroulLeGm2uhcobb6/2/Sqqtv7eq697/D5Xri3p zlgsveziC2q7+75rrboHAyzuw+FaSnHEusLq7sWp0sqwsJxiq/C8tUpcscAQ79pwyChjXC+zGzvL 8rUxZztztTVPKGiEPv8MdNBCD0100UYfjXTSSi89dAEAOw== ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0143.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
For real-number-exponent,= we approximate the real number with fractions and use the fractional = powers to approximate the real-number power.
10
10p
3.1
p»3.14159..
Example C:
31
10
The Exponential Functions
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0143_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh8QFcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADw AVsAgAAAAAAAAAL/jI+py+0Po5y02ouz3rz7D4biSJbmiabqyrbuCyPATNf2jef6zve+HfgJh7sg 8YgsJpdMgLEJjSKf0qr16jxgt1watXv8gqXicbNsTvvQ6vZV5o7/2PIavd6743X6vbnvF5gDJ+gH GHdY6KQ4xyiX6GioFflIuWjJhzmo+ceJSegJBqk2Gli6dxq6phoJyoqVKvo6E1s5a1V7Szapi2uZ izgL3HtJjOdqzDT8druc5tycfMwrrfwb/QotXP1IzT11vZ39DU5O6m0upB21Ljuerg7/hy7P036G zXoful+PXK+EUj9Y4gAGNAiLHsIbA8u907cwU0RcCifSCvdQVcNP/xar/OtYzNFGjwVBhjSZ5GPH kUNYsisJ0iU3lRZlroLpyaYincloTuR5EGLGmCjPVKyJUahSk0CJ+YzYdBNOTlFRFVV29GdSjVO1 Xk2ZFepWfl3Ffp0SdmFVhvm4Fl0rLC1CuHbakn17Fq2BvHS92M15ta9GuQYFn7y7lGheIk/VjgU8 dOVixoQBGjYcFDHTyS0r+3tMtaxjznM8y7v8NzRe0mtMw0MtWmBg1q33noUdWTVKzFRdp8OdGPJu 2nl8mwPuNjhS4kWMk0OuObpk5nycf4MuPPlm6oOszwStiTcO8WPI//JeDbtu7Yq5M0QvTX342IXd j4ffEzzH3F7t2//Bb4x8+ynXn3+0xIBgggouyGCDDj4IYWNz6UdhK7MZ6AWATlVoIX9mYZiFbV8J yCEj5nVxYisa9kKibB6OBqKE9bn4Io3bxbiiLi12SOCHGMpoWYkm0hckiCGm6A6PPQr5mpFH8sVk IUgethyOIl6oJHvZtfdjjqkJMiWV861mZZhb7CgSkZ8ZCeSaWUq3HpcGtnlalGCqWSebXuLpRphT mkmSnleSmSafdxI65541HvPlgDd2OehwNmoZ53RlQjkpnGNKeultdppi6HFO0tlkplueWiWkgDJj aqWuFphopI8OGaohWKqK6Zuobjqrf6T+9qmtixbZ6YjBWjWsm7iketoqr5r6GOuqvjTr6LMwLmss tcfWIS0U3U4jq5w7NbptfKMquiSyyY6LqK/oUnroulLeGm2uhcobb6/2/Sqqtv7eq697/D5Xri3p zlgsveziC2q7+75rrboHAyzuw+FaSnHEusLq7sWp0sqwsJxiq/C8tUpcscAQ79pwyChjXC+zGzvL 8rUxZztztTVPKGiEPv8MdNBCD0100UYfjXTSSi89dAEAOw== ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0144.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
For real-number-exponent,= we approximate the real number with fractions and use the fractional = powers to approximate the real-number power.
10
10
10p
3.14
3.1
p»3.14159..
Example C:
31
10
314
100
The Exponential Functions
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0144_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh8QFcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADw AVsAgAAAAAAAAAL/jI+py+0Po5y02ouz3rz7D4biSJbmiabqyrbuCyPATNf2jef6zve+HfgJh7sg 8YgsJpdMgLEJjSKf0qr16jxgt1watXv8gqXicbNsTvvQ6vZV5o7/2PIavd6743X6vbnvF5gDJ+gH GHdY6KQ4xyiX6GioFflIuWjJhzmo+ceJSegJBqk2Gli6dxq6phoJyoqVKvo6E1s5a1V7Szapi2uZ izgL3HtJjOdqzDT8druc5tycfMwrrfwb/QotXP1IzT11vZ39DU5O6m0upB21Ljuerg7/hy7P036G zXoful+PXK+EUj9Y4gAGNAiLHsIbA8u907cwU0RcCifSCvdQVcNP/xar/OtYzNFGjwVBhjSZ5GPH kUNYsisJ0iU3lRZlroLpyaYincloTuR5EGLGmCjPVKyJUahSk0CJ+YzYdBNOTlFRFVV29GdSjVO1 Xk2ZFepWfl3Ffp0SdmFVhvm4Fl0rLC1CuHbakn17Fq2BvHS92M15ta9GuQYFn7y7lGheIk/VjgU8 dOVixoQBGjYcFDHTyS0r+3tMtaxjznM8y7v8NzRe0mtMw0MtWmBg1q33noUdWTVKzFRdp8OdGPJu 2nl8mwPuNjhS4kWMk0OuObpk5nycf4MuPPlm6oOszwStiTcO8WPI//JeDbtu7Yq5M0QvTX342IXd j4ffEzzH3F7t2//Bb4x8+ynXn3+0xIBgggouyGCDDj4IYWNz6UdhK7MZ6AWATlVoIX9mYZiFbV8J yCEj5nVxYisa9kKibB6OBqKE9bn4Io3bxbiiLi12SOCHGMpoWYkm0hckiCGm6A6PPQr5mpFH8sVk IUgethyOIl6oJHvZtfdjjqkJMiWV861mZZhb7CgSkZ8ZCeSaWUq3HpcGtnlalGCqWSebXuLpRphT mkmSnleSmSafdxI65541HvPlgDd2OehwNmoZ53RlQjkpnGNKeultdppi6HFO0tlkplueWiWkgDJj aqWuFphopI8OGaohWKqK6Zuobjqrf6T+9qmtixbZ6YjBWjWsm7iketoqr5r6GOuqvjTr6LMwLmss tcfWIS0U3U4jq5w7NbptfKMquiSyyY6LqK/oUnroulLeGm2uhcobb6/2/Sqqtv7eq697/D5Xri3p zlgsveziC2q7+75rrboHAyzuw+FaSnHEusLq7sWp0sqwsJxiq/C8tUpcscAQ79pwyChjXC+zGzvL 8rUxZztztTVPKGiEPv8MdNBCD0100UYfjXTSSi89dAEAOw== ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0145.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
For real-number-exponent,= we approximate the real number with fractions and use the fractional = powers to approximate the real-number power.
10
10
10p
3.1415
3.141
3.14
3.1
p»3.14159..
Example C:
31
10
314
100
p
The Exponential Functions
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0145_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh8QFcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADw AVsAgAAAAAAAAAL/jI+py+0Po5y02ouz3rz7D4biSJbmiabqyrbuCyPATNf2jef6zve+HfgJh7sg 8YgsJpdMgLEJjSKf0qr16jxgt1watXv8gqXicbNsTvvQ6vZV5o7/2PIavd6743X6vbnvF5gDJ+gH GHdY6KQ4xyiX6GioFflIuWjJhzmo+ceJSegJBqk2Gli6dxq6phoJyoqVKvo6E1s5a1V7Szapi2uZ izgL3HtJjOdqzDT8druc5tycfMwrrfwb/QotXP1IzT11vZ39DU5O6m0upB21Ljuerg7/hy7P036G zXoful+PXK+EUj9Y4gAGNAiLHsIbA8u907cwU0RcCifSCvdQVcNP/xar/OtYzNFGjwVBhjSZ5GPH kUNYsisJ0iU3lRZlroLpyaYincloTuR5EGLGmCjPVKyJUahSk0CJ+YzYdBNOTlFRFVV29GdSjVO1 Xk2ZFepWfl3Ffp0SdmFVhvm4Fl0rLC1CuHbakn17Fq2BvHS92M15ta9GuQYFn7y7lGheIk/VjgU8 dOVixoQBGjYcFDHTyS0r+3tMtaxjznM8y7v8NzRe0mtMw0MtWmBg1q33noUdWTVKzFRdp8OdGPJu 2nl8mwPuNjhS4kWMk0OuObpk5nycf4MuPPlm6oOszwStiTcO8WPI//JeDbtu7Yq5M0QvTX342IXd j4ffEzzH3F7t2//Bb4x8+ynXn3+0xIBgggouyGCDDj4IYWNz6UdhK7MZ6AWATlVoIX9mYZiFbV8J yCEj5nVxYisa9kKibB6OBqKE9bn4Io3bxbiiLi12SOCHGMpoWYkm0hckiCGm6A6PPQr5mpFH8sVk IUgethyOIl6oJHvZtfdjjqkJMiWV861mZZhb7CgSkZ8ZCeSaWUq3HpcGtnlalGCqWSebXuLpRphT mkmSnleSmSafdxI65541HvPlgDd2OehwNmoZ53RlQjkpnGNKeultdppi6HFO0tlkplueWiWkgDJj aqWuFphopI8OGaohWKqK6Zuobjqrf6T+9qmtixbZ6YjBWjWsm7iketoqr5r6GOuqvjTr6LMwLmss tcfWIS0U3U4jq5w7NbptfKMquiSyyY6LqK/oUnroulLeGm2uhcobb6/2/Sqqtv7eq697/D5Xri3p zlgsveziC2q7+75rrboHAyzuw+FaSnHEusLq7sWp0sqwsJxiq/C8tUpcscAQ79pwyChjXC+zGzvL 8rUxZztztTVPKGiEPv8MdNBCD0100UYfjXTSSi89dAEAOw== ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0146.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
For real-number-exponent,= we approximate the real number with fractions and use the fractional = powers to approximate the real-number power.
   1385.45..
10
10
10
10
10p
3.1415
3.141
3.14
3.1
p»3.14159..
Example C:
31
10
314
100
3141
1000
31415
10000
p
The Exponential Functions
------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0146_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlh8QFcAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAAAAADw AVsAgAAAAAAAAAL/jI+py+0Po5y02ouz3rz7D4biSJbmiabqyrbuCyPATNf2jef6zve+HfgJh7sg 8YgsJpdMgLEJjSKf0qr16jxgt1watXv8gqXicbNsTvvQ6vZV5o7/2PIavd6743X6vbnvF5gDJ+gH GHdY6KQ4xyiX6GioFflIuWjJhzmo+ceJSegJBqk2Gli6dxq6phoJyoqVKvo6E1s5a1V7Szapi2uZ izgL3HtJjOdqzDT8druc5tycfMwrrfwb/QotXP1IzT11vZ39DU5O6m0upB21Ljuerg7/hy7P036G zXoful+PXK+EUj9Y4gAGNAiLHsIbA8u907cwU0RcCifSCvdQVcNP/xar/OtYzNFGjwVBhjSZ5GPH kUNYsisJ0iU3lRZlroLpyaYincloTuR5EGLGmCjPVKyJUahSk0CJ+YzYdBNOTlFRFVV29GdSjVO1 Xk2ZFepWfl3Ffp0SdmFVhvm4Fl0rLC1CuHbakn17Fq2BvHS92M15ta9GuQYFn7y7lGheIk/VjgU8 dOVixoQBGjYcFDHTyS0r+3tMtaxjznM8y7v8NzRe0mtMw0MtWmBg1q33noUdWTVKzFRdp8OdGPJu 2nl8mwPuNjhS4kWMk0OuObpk5nycf4MuPPlm6oOszwStiTcO8WPI//JeDbtu7Yq5M0QvTX342IXd j4ffEzzH3F7t2//Bb4x8+ynXn3+0xIBgggouyGCDDj4IYWNz6UdhK7MZ6AWATlVoIX9mYZiFbV8J yCEj5nVxYisa9kKibB6OBqKE9bn4Io3bxbiiLi12SOCHGMpoWYkm0hckiCGm6A6PPQr5mpFH8sVk IUgethyOIl6oJHvZtfdjjqkJMiWV861mZZhb7CgSkZ8ZCeSaWUq3HpcGtnlalGCqWSebXuLpRphT mkmSnleSmSafdxI65541HvPlgDd2OehwNmoZ53RlQjkpnGNKeultdppi6HFO0tlkplueWiWkgDJj aqWuFphopI8OGaohWKqK6Zuobjqrf6T+9qmtixbZ6YjBWjWsm7iketoqr5r6GOuqvjTr6LMwLmss tcfWIS0U3U4jq5w7NbptfKMquiSyyY6LqK/oUnroulLeGm2uhcobb6/2/Sqqtv7eq697/D5Xri3p zlgsveziC2q7+75rrboHAyzuw+FaSnHEusLq7sWp0sqwsJxiq/C8tUpcscAQ79pwyChjXC+zGzvL 8rUxZztztTVPKGiEPv8MdNBCD0100UYfjXTSSi89dAEAOw== ------=_NextPart_01C980C1.3B253F30 Content-Location: file:///C:/D1545AF3/1ExponentialFunctionsandCompoundInterests_files/slide0147.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" The Exponential Function
For real-number-exponent,= we approximate the real number with fractions and use the fractional = powers to approximate the real-number power.
   1385.45..
10
10
10
10
10p
3.1415
3.141
3.14
3.1
p»3.14159..
Example C:
31
10
314
100