Question

The population of an endangered species of insect is 480,000. The population decreases at the rate of 10% per year. Identify the exponential decay function to model the situation. Then find the population of the species after 3 years.

Answer 1

function: P = 480000 * (0.9)^t

after 3 years: P = 349,920

Explanation:

First we need to know the model of an exponencial equation:

P = Po * (1 + r)^t

Where P is the final value after t years, Po is the inicial value and r is the rate.

In this case, we have Po = 480000 and r = -10% = -0.1 (negative because it is a decay and not a growth), so the equation is:

P = 480000 * (1 - 0.1)^t

P = 480000 * (0.9)^t

If we have t = 3 years, the final population is:

P = 480000 * (0.9)^3 = 349920