document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=204458>Question 204458</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Time (h)	0,	8,	16,	24,	32,	40,	48<BR>\n" );
document.write( "Amount (g)	4.84,	4.63,	4.52,	4.45,	4.33,	4.19,	4.08\r<BR>\n" );
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document.write( "(a) Find an appropriate exponential model of the data points.\r<BR>\n" );
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document.write( "Amount at time t, A(t) = \r<BR>\n" );
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document.write( "I know I have to make two equations y=Ca^x <BR>\n" );
document.write( "would someone be able to explain the steps please? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #154355 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=154355\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Time (h) 0, 8, 16, 24, 32, 40, 48<BR>\n" );
document.write( "Amount (g) 4.84, 4.63, 4.52, 4.45, 4.33, 4.19, 4.08 <BR>\n" );
document.write( "(a) Find an appropriate exponential model of the data points. <BR>\n" );
document.write( "Amount at time t, A(t) = <BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "Pick any two points like (8,4.63) and (16,4.52)<BR>\n" );
document.write( "Substitute those value into A(t) = a*b^x<BR>\n" );
document.write( "4.52 = a*b^16<BR>\n" );
document.write( "4.63 = a*b^8<BR>\n" );
document.write( "-----<BR>\n" );
document.write( "Divide the equation with the lower power into the one with the higher power<BR>\n" );
document.write( "to get rid of \"a\" and to solve for \"b\":<BR>\n" );
document.write( "You get b^8 = 0.9762<BR>\n" );
document.write( "Therefore b = 0.9970<BR>\n" );
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document.write( "Substitute a known b-value into either equation to solve for \"a\":<BR>\n" );
document.write( "4.63 = a*b^8<BR>\n" );
document.write( "4.63 = a*0.9762<BR>\n" );
document.write( "a = 4.7429<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "Equation:<BR>\n" );
document.write( "A(t) = 4.7429*(0.9970)^x<BR>\n" );
document.write( "==================================<BR>\n" );
document.write( "Comment: I could have made this easier if I had chosen the<BR>\n" );
document.write( "point with x=0 but I wanted to illustrate the general <BR>\n" );
document.write( "procedure.<BR>\n" );
document.write( "If you calculate the A(t) values using the equation you will<BR>\n" );
document.write( "see that they differ slightly from the data you were given.<BR>\n" );
document.write( "That is because I rounded off the values of both a and b.<BR>\n" );
document.write( "======================================\r<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
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