precalc question

Question

The cities of Abnarca and Bonipto have populations that are growing exponentially. In 1980, Abnarca had a population of 25,000 people. In 1990, its population was 29,000. Bonipto had a population of 34,000 in 1980. The population of Bonipto doubles every 55 years.

(a) How long does it take the population of Abnarca to double?

(b) When will Abnarca’s population equal that of Bonipto?

Answer 1

Let A(t) and B(t) be the populations of Abnarca and Bonipto, respectively, where t is the number of years since 1980. Therefore, 1980 is t = 0. 29,000 divided by 25,000 is 1.16, so we can assume Abnarca's population increases by 16% every 10 years. Therefore:

A(t) = 25000 * 1.16^t/10

B(t) = 34000 * 2^t/55

for part a), set A(t) = 50000, use log rules to solve for t.

for part b), set A(t) = B(t), use log rules to solve for t.