In 1990 a town's population was 21354. In 1998 the town's population increased to 29012. Assuming that the population increased exponentially the one-year growth factor is 1.039.

Question

Quizplus · Accepted Answer

To check if the population increased exponentially, we can calculate the annual growth rate using the formula:

r = (P2/P1)^(1/n) - 1

where r is the annual growth rate, P1 is the initial population, P2 is the final population, and n is the number of years between the two population counts.

In this case, we have:

P1 = 21354
P2 = 29012
n = 8 (since the population count is for 1990 and 1998, which is a span of 8 years)

Plugging these values into the formula, we get:

r = (29012/21354)^(1/8) - 1
r = 0.039
r = 3.9%

Since the annual growth rate is constant at 3.9%, we can say that the population increased exponentially. The one-year growth factor is therefore:

1 + r = 1 + 0.039 = 1.039

So the statement is true.

In 1990 a Town's Population Was 21354