For the exponential function f , the table above shows several values of x and their corresponding values of ,

Question

For the exponential function f , the table above shows several values of x and their corresponding values of , where a is a constant greater than 1. If k is a constant and , what is the value of k ?

Accepted Answer

The correct answer is 8. The values of for the exponential function f shown in the table increase by a factor of for each increase of 1 in x . This relationship can be represented by the equation , where b is a constant. It&rsquo;s given that when , . Substituting 2 for x and for into yields . Since , it follows that . Thus, an equation that defines the function f is . It follows that the value of k such that can be found by solving the equation , which yields .

$x$	$f of x$
$1$	$a$
$2$	$a, to the fifth power.$
$3$	$a, to the ninth power$

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