Question 1155242
<br>
{{{y = ab^x}}}<br>
Use the two given data points:<br>
{{{54 = ab^(-2)}}}
{{{2/3 = ab^2}}}<br>
Divide the second equation by the first:<br>
{{{1/81 = b^4}}}
{{{1/3 = b}}}<br>
Note if this were a geometric sequence problem, the value of b could be either 1/3 or -1/3.  But for an exponential function, b has to be positive.<br>
Substitute this value of b in either original equation to find a.<br>
{{{2/3 = a(1/3)^2}}}
{{{2/3 = a/9}}}
{{{a = 9(2/3) = 6}}}<br>
ANSWER: One possible function for the two given points is {{{y = 6(1/3)^x}}}<br>