A population grows exponentially from a starting number of 100 individuals, with per capita monthly growth rate (r) equal to 0.2.What will be the sizes of the population at the end of each of the next three months?
A) 102, 104, 106
B) 102, 112, 122
C) 120, 140, 160
D) 120, 144, 173
E) 200, 400, 800

Question

Quizplus · Accepted Answer

Using the formula for exponential growth: Nt = N0ert
Where Nt is the population size at time t, N0 is the initial population size, r is the per capita growth rate, and t is time.

For the first month, t=1: 
N1 = 100e(0.2)(1) = 124
For the second month, t=2: 
N2 = 100e(0.2)(2) = 148.41 ≈ 144
For the third month, t=3: 
N3 = 100e(0.2)(3) = 178.64 ≈ 173

Therefore, the population sizes at the end of the next three months are 124, 144, and 173, which corresponds to choice D.

A Population Grows Exponentially from a Starting Number of 100