How Fast Will the Sloth Population Grow in 10 Years?

What is the intrinsic rate of increase for the sloth population introduced to the national park?

a) 3.5%

b) 0.035

c) 35%

d) 3.5

The intrinsic rate of increase for the sloth population introduced to the national park is:

b) 0.035

The intrinsic rate of increase is a measure of the maximum growth rate that a population can achieve under ideal conditions. In this case, the intrinsic rate of increase for the sloth population in the national park is 0.035, meaning they will grow by 3.5% every year under ideal conditions.

By utilizing the formula Nt = N0 x e^(rt) for exponential growth, where Nt is the population size after time t, N0 is the initial population size, e is the base of the natural logarithm, r is the intrinsic rate of increase, and t is the time in years, we can calculate the population size after 10 years.

Substituting the values for the sloth population (N0 = 150, r = 0.035, t = 10), we get Nt = 150 x e^(0.035 x 10) = 150 x e^(0.35) = 150 x 1.419 = 212.85. Rounded off, the population size after 10 years will be 213.

Therefore, the population size of sloths in the national park will be 213 after 10 years of exponential growth.