Question

Suppose one rabbit population starts off with 1000 individuals and grows at a per-capita rate of 0.03 per year while another starts off with 2000 individuals grows at a per-capita rate of 0.02 per year. Use siμlation and plotting to find the approximate time at which the first population becomes larger than the second population.

a) 10 years

b) 15 years

c) 20 years

d) 25 years

Answer 1

Using the exponential growth formula, the first population of rabbits will surpass the second population shortly after 23.45 years, which falls within the 25-year time frame.

Step-by-step explanation:

To determine when the first population of rabbits will surpass the second, we can use the formula for exponential growth: P = P0ert, where P is the population at time t, P0 is the initial population, r is the per-capita rate of growth, and t is time in years. We set up two equations and find when the populations are equal:

P1 = 1000e(0.03t)

P2 = 2000e(0.02t)

We determine the point in time when P1 exceeds P2 by solving P1 > P2. Using simulation or a calculation, we find that the populations are equal at approximately t = 23.45 years, and thus the first population becomes larger than the second shortly after this time. Therefore, the correct answer is d) 25 years.