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
[tex]\left|\begin{array}{c|c}x&y\\--&--\\1&9\\2&6\\3&4\\4&\dfrac83\\\\5&\dfrac{16}{9}\end{array}\right|[/tex]
Answer:
(B) [tex]\dfrac{2}{3}[/tex]
Step-by-step explanation:
An exponential function is a function of the form
[tex]y= a (b)^{x}[/tex]
where a is the initial value and b is the multiplicative rate of change
When x=2, y=6, we have:
[tex]6= a (b)^{2}[/tex]
When x=3, y=4, we have:
[tex]4= a (b)^{3}[/tex]
Dividing the two equations:
[tex]\dfrac{a (b)^{3}}{a (b)^{2}} =\dfrac{6}{9} \\b=\dfrac{6}{9}\\b=\dfrac{2}{3}[/tex]
The multiplicative rate of change, b is [tex]\dfrac{2}{3}[/tex].
The correct option is B.
