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