Question

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

Answer 1

Answer:

$f(12) = 323.02$

$f(12) = 16.7 * 1.28^{12$

Step-by-step 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:

$f(x) = ab^x$

$f(12) = 16.7 * 1.28^{12$

$f(12) = 323.02$