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If f (2) is an exponential function where f(-2.5) = 9 and f(7) = 91, then find

the value of f(12), to the nearest hundredth.

User Nclark
by
7.9k points

1 Answer

4 votes

Answer:


f(12) = 323.02


f(12) = 16.7 * 1.28^{12

Explanation:

Given


f(-2.5) = 9


f(7) = 91


f(12) = 16.7 * 1.28^{12

Required


f(12)

An exponential function is:


f(x) = ab^x


f(-2.5) = 9 implies that:


9 = ab^(-2.5)


f(7) = 91 implies that:


91 = ab^7

Divide both equations


91/9 = ab^7/ab^(-2.5)


91/9 = b^7/b^(-2.5)

Apply law of indices


91/9 = b^(7+2.5)


10.11 = b^(9.5)

Take 9,5th root of both sides


b = 1.28

So, we have:


9 = ab^(-2.5)


9 = a * 1.28^(-2.5)


9 = a * 0.54


a = 9/0.54


a = 16.7

f(12) is calculated as:


f(x) = ab^x


f(12) = 16.7 * 1.28^{12


f(12) = 323.02

User Johannes Dorn
by
8.9k points

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