Question

The population of a town is 345,000. The function

f(t) = 345,000(1.2)^t gives the predicted population of the
town in t years. Approximately what will the population be
in 3 years?

Answer 1

600,000

Explanation:

The mathematical concept demonstrated in this question is the process of exponential growth. Exponential growth demonstrates an increase in quantity by a percentage or factor over time. It is represented by the general formula
`f(x) = a(1+r)^(x)` where a is the initial amount, r is the growth rate, and x is the time interval expressed as an integer.

For this problem, we can see that the initial population of the town is 345,000, and it increases by a rate of 20% each year. We can determine that the growth rate is 20% because 1 + r = 1.2, so r must be equal to .20 (or 20%). We are given that t = 3, so we can plug that value in to the function given.

• f(3) = 345,000(1.2)³
• f(3) = 345,000(1.728)
• f(3) = 596,160

We calculate the population in 3 years to be 596,160. This can be approximated to 600,000.