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densk [106]
3 years ago
11

If f(x) is an exponential function where f(-2,5) = 9 and f(7) = 91, then find the value of f(12), to the nearest hundredth.

Mathematics
1 answer:
insens350 [35]3 years ago
7 0

Answer:

f(12) = 323.02

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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