Question

If f(x) is an exponential function where f(-1.5) 26 and

f(5.5) = 7, then find the value of f(10), to the nearest hundredth.

Answer 1

`f(10) = 1147.25`

Explanation:

Given

`f(-1.5) = 26`

`f(5.5) = 7`

Required

f(10)

An exponential function is represented as:

`f(x) = ab^x`

`f(-1.5) = 26` impleies that:

`26 = ab^(-1.5)` --- (1)

`f(5.5) = 7` implies that

`7 = ab^(5.5)` --- (2)

Divide (2) by (1)

`26/7 = ab^(-1.5)/ab^(5.5)`

`3.71429 = b^(-1.5+5.5)`

`3.71429 = b^(4)`

Take 4th root

`b = 1.39`

Substitute
`b = 1.39` in
`26 = ab^(-1.5)`

`26 = a * 1.39^(-1.5)`

`26 = a * 0.6102`

Solve for (a)

`a = 26/0.6102`

`a = 42.61`

f(10) is calculated as:

`f(10) = ab^(10)`

`f(10) = 42.61 * 1.39^(10)`

`f(10) = 1147.25`