Solve. Round the answer to the nearest whole.
-If the annual population growth rate is 5.2%, find how long will it take a population of birds to increase from 400 birds to 1100 birds.
A) 5 yr
B) 108 yr
C) 135 yr
D) 19 yr

Question

Quizplus · Accepted Answer

The problem can be solved using the formula for exponential growth: $ P = P_0 \times (1 + r)^t $, where $ P $ is the future population, $ P_0 $ is the initial population, $ r $ is the growth rate (as a decimal), and $ t $ is the time in years. Rearranging the formula to solve for $ t $, we get $ t = \frac{\log(P/P_0)}{\log(1+r)} $. Substituting $ P = 1100 $, $ P_0 = 400 $, and $ r = 0.052 $ into the formula gives $ t \approx 18.6 $ years, which rounds to 19 years.

Solve. Round the Answer to the Nearest Whole