Question

In 2020, the population of a small town was 8,000. The population is increasing at a rate of 4.3% per year. Rewrite an exponential growth function to find the monthly and quarterly rates.

Answer 1

The exponential growth function for the population can be written as:

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

Where:

P0 = initial population = 8,000

r = annual growth rate = 4.3% = 0.043

To find the monthly rate, we need to divide the annual rate by 12 (since there are 12 months in a year):

r_monthly = r/12 = 0.043/12 = 0.00358

So the exponential growth function with monthly growth rate becomes:

P(t) = 8000 * e^(0.00358t)

To find the quarterly rate, we need to divide the annual rate by 4 (since there are 4 quarters in a year):

r_quarterly = r/4 = 0.043/4 = 0.01075

So the exponential growth function with quarterly growth rate becomes:

P(t) = 8000 * e^(0.01075t)