Consider a population of rabbits that has an initial population size of 10 individuals (N₀ = 10). Let’s assume that the intrinsic rate of growth for a rabbit is r = 0.5 (or 50 percent), which means that each rabbit produces a net increase of 0.5 rabbits each year. With this information, we can predict the size of the rabbit population 2 years from now:

N_t = N₀e^rt

N_t = 10 × e^0.5×2

N_t = 10 × e¹

N_t = 10 × (2.72)¹

N_t = 10 × 2.72

N_t = 27 rabbits

We can then ask how large the rabbit population will be after 4 years:

N_t = 10 × e^0.5×4

N_t = 10 × e²

N_t = 10 × (2.72)²

N_t = 10 × 7.4

N_t = 74 rabbits

We can also project the size of the rabbit population 10 years from now:

N_t = 10 × e^0.5×10

N_t = 10 × e⁵

N_t = 10 × (2.72)⁵

N_t = 10 × 148.9

N_t = 1,489 rabbits

Your Turn Now assume that the intrinsic rate of growth is 1.0 for rabbits. Calculate the predicted size of the rabbit population after 1, 5, and 10 years. Create a graph that shows the growth curves for an intrinsic rate of growth at 0.5, as calculated above, and an intrinsic rate of growth at 1.0. (Note that you will need to use your calculator to complete this problem.)