Answer :
The exponential function f(x) can represent growth or decay
The value of f(14) is 226.07
How to determine the value of f(14)?
The given parameters are:
f(-2) = 25 and f(7) = 85
An exponential function is represented as:
f(x) = ab^x
So, we have:
ab^-2 = 25
Also, we have:
ab^7 = 85
Divide both equations.
This gives
b^9 = 3.4
Take the 9th root of both sides
b = 1.15
Recall that:
ab^7 = 85
This gives
a* 1.15^7 = 85
Solve for a
a = 31.95
So, the exponential function is:
f(x) = 31.95 * 1.15^x
Substitute 14 for x
f(14) = 31.95 * 1.15^14
f(14) = 226.07
Hence, the value of f(14) is 226.07
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