Answer:
the growth factor is 4
Step-by-step explanation:
We are given f(x) is exponential function
so,
[tex]f(x)=a(b)^x[/tex]
where
a is the initial value
b is output value increase as each input value increases by 1
so, we have to find 'b'
we can select any two points and then find 'b'
At x=1 , f(x)=4:
we can plug these values
[tex]4=a(b)^1[/tex]
At x=3 , f(x)=64:
we can plug these values
[tex]64=a(b)^3[/tex]
now, we can divide both equations
and we get
[tex]\frac{64}{4} =\frac{a(b)^3}{a(b)^1}[/tex]
we can simplify it
[tex]16 =b^2[/tex]
[tex]b=4[/tex]
So, the growth factor is 4