Question

The table represents an exponential function.

Answer 1

Question Correction

The table represents an exponential function. What is the multiplicative rate of change of the  function?

(A)1/3 (B)2/3 (C)2 (D)9

$\left|\begin{array}{c|c}x&y\\--&--\\1&9\\2&6\\3&4\\4&\dfrac83\\\\5&\dfrac{16}{9}\end{array}\right|$

Answer:

(B)  $\dfrac{2}{3}$

Step-by-step explanation:

An exponential function is a function of the form

$y= a (b)^{x}$

where a is the initial value and b is the multiplicative rate of change

When  x=2, y=6, we have:

$6= a (b)^{2}$

When  x=3, y=4, we have:

$4= a (b)^{3}$

Dividing the two equations:

$\dfrac{a (b)^{3}}{a (b)^{2}} =\dfrac{6}{9} \\b=\dfrac{6}{9}\\b=\dfrac{2}{3}$

The multiplicative rate of change, b is $\dfrac{2}{3}$.

The correct option is B.