Question 718152
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The function has the form {{{y=ae^(-bx)}}}<br>
The two given data points are (0.6,1000) and (1.8,1), giving us these two equations:<br>
{{{1000=ae^(-0.6b)}}}
{{{1=ae^(-1.8b)}}}<br>
Dividing the first equation by the second will eliminate a, giving us an equation we can solve to find b.<br>
{{{1000=e^(1.2b)}}}
{{{ln(1000)=1.2b}}}
{{{b=ln(1000)/1.2)}}}<br>
A calculator then gives the value of b to several decimal places as 5.75646...<br>
Use that value of b in the second equation to get an equation we can solve to find the value of a.<br>
{{{1=ae^(-1.8b)}}}<br>
{{{a=1/e^(-1.8b)=e^(1.8b)}}}<br>
Using a calculator then gives the value of a to several decimal places as 31622.7766....<br>
ANSWERS (to several decimal places):
a = 31622.7766
b = 5.75646<br>
Graphing this function on a graphing calculator confirms the two given data points (0.6,1000) and (1.8,1).<br>
Found using a different path than that used by the other tutor, this matches his answers -- except that currently he has a typo in the leading digit of the value for a.<br>