If f(x) is an exponential function where f(5) = 3 and f(11) = 28, then find the value of f(8), to the nearest hundredth.

f(x) is an exponential function, so .

f(11) = 28 tells us    

f(5) = 3 tells us        

If we divide those equations, we'd have   

This simplifies to

Take the sixth root of both sides and you have

     (technically it is ±, but b>0 for exponential functions)

Now using that, we have .

Take a deep breath...

OK, we plug in 5 and 3 one more time to find a.

Divide by that mess on the left and you'll have a.

And out function is .

Wow, that's ugly.

You could use exponent rules to simplify this a bit:

Now evaluate f(8) by putting 8 in for x and you'll get 9.16515138991, or 9.17 to the nearest hundredth.

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(8+64)^2= 5184 < answer

step-by-step explanation:

2^3 = 8

4^3= 64

(8+64)^2 = 5184