<PRE><B>Question 1129326</B>
&lt;br&gt;
The general form of an exponential equation is&lt;br&gt;
{{{f(x) = ab^x}}}&lt;br&gt;
Given f(8)=320 and f(26)=1200, we have&lt;br&gt;
{{{ab^8=320}}}
{{{ab^26=1200}}}&lt;br&gt;
Divide the 2nd equation by the first to eliminate a:&lt;br&gt;
{{{b^18 = 1200/320 = 15/4 = 3.75}}}
{{{b = 3.75^(1/18)}}}&lt;br&gt;
Use that value in either original equation to find the value of a:&lt;br&gt;
{{{a(3.75)^(8/18) = 320}}}
{{{a = 320/((3.75^(8/18)))}}} = 177.84 to 2 decimal places.&lt;br&gt;
We now have the a and b values for the exponential function.&lt;br&gt;
ANSWER: {{{f(x) = 177.84(3.75^(x/18))}}}&lt;br&gt;
Check on a graphing calculator:
f(8) = 320.0033
f(26) = 1200.0124&lt;br&gt;
The small error of course because of the rounding of the value of a.</PRE>