Question

A town has a population of 16000 and grows at 2.5% every year. To the nearest tenth of a year, how long will it be until the population will reach 23300?

Answer 1

15.2 years

Explanation:

Let t be the time (in years) it takes for the population to reach 23300. We can use the formula for exponential growth:

A = P(1 + r/100)^t

where A is the final amount, P is the initial amount, r is the annual growth rate, and t is the time in years.

We know that the initial population P is 16000, the annual growth rate r is 2.5%, and the final population A is 23300. Substituting these values into the formula, we get:

23300 = 16000(1 + 2.5/100)^t

Simplifying this equation, we get:

(1 + 0.025)^t = 23300/16000

1.025^t = 1.45625

Taking the natural logarithm of both sides, we get:

ln(1.025^t) = ln(1.45625)

t ln(1.025) = 0.37604

t = 0.37604 / ln(1.025)

t ≈ 15.2

Therefore, it will take about 15.2 years (rounded to the nearest tenth of a year) for the population to reach 23300.