jadeafrias

15.03.2022 •

Mathematics

What is the x-intercept of the function graphed below? (4,0)

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Ответ:

860jay

23.05.2021

Mathematics

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

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