If f ( x ) f(x) is an exponential function where f ( − 5 ) = 26 f(−5)=26 and f ( 3 ) = 54 f(3)=54, then find the value of f ( 0.5 ) f(0.5), to the nearest hundredth.

Step-by-step explanation:

Given

Required

Find f(0.5)

An exponential function is of the form:

For:

So, we have:

--- (1)

For

So, we have:

--- (2)

Divide (2) by (1)

Apply law of indices

Take 8th roots of both sides

Substitute 1.10 for b in

Solve for a

To solve for f(0.5), we have:

(approximated)

correct answers below: