Question

The table represents an exponential function.

Answer 1

Answer:

b=2/3

Step-by-step explanation:

The table is given as:

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

The exponential function is given in the form

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

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

When  x=1, y=9, we have:

$9= a (b)^{1}$

When  x=3, y=4, we have:

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

Dividing the two equations:

$\dfrac{a (b)^{3}}{a (b)^{1}} =\dfrac{4}{9} \\b^2=\dfrac{4}{9}\\b=\sqrt{\dfrac{4}{9}} \\b=\dfrac{2}{3}$

The multiplicative rate of change, b is 2/3.