Question

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.

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