Question

Function f if an exponential function.

By what factor does the output value increase as each input value increases by 1?

x: -1, 1, 3, 5, 7
f(x): 1/4, 6, 64, 1024, 16234

Answer 1

the growth factor is 4

Explanation:

We are given f(x) is exponential function

so,

`f(x)=a(b)^x`

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

`4=a(b)^1`

At x=3 , f(x)=64:

we can plug these values

`64=a(b)^3`

now, we can divide both equations

and we get

`(64)/(4) =(a(b)^3)/(a(b)^1)`

we can simplify it

`16 =b^2`

`b=4`

So, the growth factor is 4