You are studying a population of beetles of size N = 3000. During a 1-month period, you record 400 births and 150 deaths. Considering the estimate of r from these data, project the population size in 6 months.

Question

Quizplus · Accepted Answer

First, we need to calculate the intrinsic growth rate (r) of the beetle population using the formula:

r = (ln(Nt) - ln(N0)) / t

where N0 is the initial population size, Nt is the population size after a certain period of time, and t is the length of that period.

In this case, N0 = 3000, Nt = 3000 + 400 - 150 = 3250 (i.e., the initial population size plus the number of births minus the number of deaths), and t = 1 month. Substituting these values into the formula, we get:

r = (ln(3250) - ln(3000)) / 1 = 0.0805

Next, we can use the exponential growth equation to project the population size after 6 months:

Nt = N0 * e^(rt)

where e is the base of the natural logarithm (approximately 2.71828).

Substituting N0 = 3250, r = 0.0805, and t = 6 months, we get:

Nt = 3250 * e^(0.0805 * 6) = 4944.94

Rounding to the nearest integer, the projected population size in 6 months is 4945, which corresponds to choice C.

You Are Studying a Population of Beetles of Size N