We are given initial value of the function =108.
Therefore, f(0) = 108.
Let us find some values of the function to graph it.
[tex]\\f_1=f(1)=\dfrac{2}{3}f(0)= \dfrac{2}{3}\cdot 108=72,\\f_2=f(2)=\dfrac{2}{3}f(1)= \dfrac{2}{3}\cdot 72=48,\\ f_3=f(3)=\dfrac{2}{3}f(2)= \dfrac{2}{3}\cdot 48=32[/tex]
Therefore, some of the terms of the sequence would be
108, 72, 48, 32...
We can see that function is decreasing exponentially by factor of 2/3.
Therefore, function would be [tex]y=108(2/3)^x[/tex]
Now, we can plot the graph for exponential function [tex]y=108(2/3)^x[/tex]
