Question

A population of bears originally numbers 52000. After 5 years of growth at the same rate each year, the population has grown to 77014 . Find the annual growth rate as a percentage. %

Answer 1

The original bear population grows at an annual rate of approximately 8.2% to reach the final population over the course of 5 years.

Step-by-step explanation:

The subject of this problem is exponential growth, which describes situations where a quantity increases by the same percentage each period. In this case, the quantity is the bear population, which begins at 52000 bears and grows over 5 years to 77014 bears. The goal is to find the annual growth rate, expressed as a percentage.

To find this, we can set up an equation based on the formula for exponential growth: P = P0*(1 + r)^t. P0 is the original population, P is the final population, r is the annual growth rate we're trying to find, and t is time in years.

77014 = 52000*(1 + r)^5 We want to isolate r, so we'll divide both sides by 52000 and then take the 5th root to get :

(77014/52000)^(1/5) - 1 = r

This gives us an annual growth rate of approximately 0.082, or 8.2%.

Learn more about Exponential Growth