Respuesta :

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