Question 1164989
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The general exponential function is<br>
{{{f(x) = ab^x}}}<br>
Make two equations in a and b using the two data points.<br>
{{{1/27 = ab^2}}}
{{{27 = ab^(-1)}}}<br>
In both equations, the coefficient is a, so dividing one equation by the other will give you an equation in b only.  (That's a standard procedure for finding an exponential function given two data points.)<br>
{{{(1/27)/27= b^3}}}
{{{1/729 = b^3}}}
{{{b = 1/9}}}<br>
Use that value with either data point to determine the coefficient a.<br>
{{{1/27 = a((1/9)^2)}}}
{{{1/27 = a/81}}}
{{{a = 3}}}<br>
ANSWER: {{{f(x) = ab^x = 3((1/9)^x)}}}<br>