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:
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