If a population of 100 birds increases to 120 birds in a year, what is r?

Question

Quizplus · Accepted Answer

The formula for exponential growth is: Nt = N0 * e^(rt)
where N0 is the initial population, Nt is the population after time t, e is Euler's constant (approximately 2.718), and r is the annual growth rate.

In this case, N0 = 100, Nt = 120, and t = 1 year. Plugging in these values, we get:
120 = 100 * e^(r*1)
Simplifying:
1.2 = e^r
Taking the natural logarithm of both sides:
ln(1.2) = r
Using a calculator or estimation, ln(1.2) is approximately 0.1823, which is closest to answer choice B: 0.20.

If a Population of 100 Birds Increases to 120 Birds