The calculated value of the function f(6.5) is 1020.17
How to determine the value of f(6.5)
From the question, we have the following parameters that can be used in our computation:
f(4) = 15
f(5) = 50
An exponential function is represented as
f(x) = abˣ
Where
a = initial value
b = rate
Using the above as a guide, we have the following:
ab³ = 15
ab⁴ = 50
Divide the equations
b = 50/15
b = 3.33
So, we have
a(3.33)⁴ = 50
a = 50/(3.33)⁴
a = 0.41
So, we have
f(x) = 0.41 * (3.33)ˣ
When x = 6.5, we have
f(6.5) = 0.41 * (3.33)⁶⁻⁵
Evaluate
f(6.5) = 1020.17
Hence, the value of f(6.5) is 1020.17