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If \( f(x) \) is an exponential function where \( f(3) = 11 \) and \( f(5.5) = 57 \), then find the value of \( f(10.4) \), to the nearest hundredth.

Answer :

Solving a system of equations we can find the exponential function, then we can evaluate it to get:

f(10.4)= 1,427.2

How to find the value of f(10.4)?

We know that f(x) is a exponential function, then we can write it as:

f(x) = A*b^x

First, we know that:

f(3) = 11

f(5.5) = 57

Then we can write a system of equations:

11 = A*b^3

57 = A*b^5.5

Taking the quotient between the two equations we will get:

57/11 = (A*b^5.5)/(A*b^3)

5.18 = b^(5.5 - 3)

5.18 = b^2.5

Solving for b we will get:

(5.18)^(1/2.5) = b

1.93 = b

with that, we can get the value of b.

11 = A*(1.93)^3

A = 11/(1.93)^3

A = 1.53

So the function is:

f(x)= 1.53*(1.93)^x

Then:

f(10.4) = 1.53*(1.93)^10.4 = 1,427.2

Learn more about exponential functions at:

https://brainly.com/question/2456547

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