After the closing of the mill, the town of Sawyerville experienced a decline in its population.

The relationship between the elapsed time, t, in years, since the closing of the mill, and the town's

population, P (t), is modeled by the following function.

P (t) = 12,000 - 2^-t/15

In how many years will Sawyerville's population be 9000?

Round your answer, if necessary, to the nearest hundredth.

Question

Mathematics

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22 March, 15:05

After the closing of the mill, the town of Sawyerville experienced a decline in its population.

The relationship between the elapsed time, t, in years, since the closing of the mill, and the town's

population, P (t), is modeled by the following function.

P (t) = 12,000 - 2^-t/15

In how many years will Sawyerville's population be 9000?

Round your answer, if necessary, to the nearest hundredth.

+3

Answers (1)

Know the Answer?

Mercedes Pope · Answer 1

Step-by-step explanation:

P (t) = 12,000 (2) ^ (-t/15)

9,000 = 12,000 (2) ^ (-t/15)

0.75 = 2^ (-t/15)

ln (0.75) = ln (2^ (-t/15))

ln (0.75) = (-t/15) ln (2)

-15 ln (0.75) / ln (2) = t

t = 6.23