Question

If f (2) is an exponential function where f(-2.5) = 9 and f(7) = 91, then find

the value of f(12), to the nearest hundredth.

Answer 1

`f(12) = 323.02`

`f(12) = 16.7 * 1.28^{12`

Explanation:

Given

`f(-2.5) = 9`

`f(7) = 91`

`f(12) = 16.7 * 1.28^{12`

Required

`f(12)`

An exponential function is:

`f(x) = ab^x`

`f(-2.5) = 9` implies that:

`9 = ab^(-2.5)`

`f(7) = 91` implies that:

`91 = ab^7`

Divide both equations

`91/9 = ab^7/ab^(-2.5)`

`91/9 = b^7/b^(-2.5)`

Apply law of indices

`91/9 = b^(7+2.5)`

`10.11 = b^(9.5)`

Take 9,5th root of both sides

`b = 1.28`

So, we have:

`9 = ab^(-2.5)`

`9 = a * 1.28^(-2.5)`

`9 = a * 0.54`

`a = 9/0.54`

`a = 16.7`

f(12) is calculated as:

`f(x) = ab^x`

`f(12) = 16.7 * 1.28^{12`

`f(12) = 323.02`