In 1990 a town's population was 24382. In 1998 the town's population increased to 30608. Assuming that the population increased exponentially the population in 2006 was 38424.

Question

Quizplus · Accepted Answer

If the population increased exponentially from 1990 to 1998, we can use the formula for exponential growth:

P(t) = P0 * e^(r*t)

where P(t) is the population at time t, P0 is the initial population, r is the annual growth rate, and t is the time in years.

We can solve for r by using the information given:

30608 = 24382 * e^(r*8)
e^(r*8) = 30608/24382
r*8 = ln(30608/24382)
r = ln(30608/24382) / 8
r ≈ 0.0346 (rounded to four decimal places)

Now we can use this growth rate to find the population in 2006:

P(16) = 24382 * e^(0.0346*16)
P(16) ≈ 38424.02

So the statement is true, the population in 2006 was approximately 38424.

In 1990 a Town's Population Was 24382