Question

A population of 30 mice is released in a wildlife region. The population doubles each year for 4 years. What is the population after 4 years?

Short answer

The population of mice after 4 years is 480.

Step-by-step solution

Understand the situation

The population starts at 30 mice and doubles every year, which is a basic example of exponential growth. Given is that this happens over a period of 4 years.

Apply the exponential growth formula

In general, the formula for exponential growth can be defined as the initial value times growth rate to the power of the duration, this can be written as: \(N = N0 * 2^t\). Where \(N\) is the final population, \(N0\) is the initial population, and \(t\) is the time, which is 4 years in our case.

Substitute the given values and solve

Substitute the given values \(N0 = 30\) and \(t = 4\) into the equation. \(N = 30 * 2^4\). Compute \(2^4 = 16\), then multiply \(30 * 16 = 480\).