Question

You survey an annually breeding butterfly population and discover 1,000 females. The next year, you count 1,200 females in the same area.

1. What is the finite rate of increase, λ?
2. What will the population be five years from now if the rate of increase is the same each year?

Answer 1

The finite rate of increase, λ, is calculated as (Nt+1 / Nt) where Nt+1 is the population size in the following year and Nt is the population size in the current year. The population of butterflies increased from 1,000 to 1,200, resulting in a λ value of 1.2.

Step-by-step explanation:

The finite rate of increase, λ, can be calculated using the formula:

λ = (Nt+1 / Nt)

Where Nt+1 is the population size in the following year and Nt is the population size in the current year.

In this case, the population of butterflies increased from 1,000 to 1,200. Plugging these values into the formula:

λ = (1,200 / 1,000) = 1.2

Therefore, the finite rate of increase is 1.2.

To calculate the population five years from now, we can use the formula:

Nt+5 = Nt * λ^5

Where Nt is the current population size and λ is the finite rate of increase.

Using the given information, Nt = 1,200 and λ = 1.2:

Nt+5 = 1,200 * (1.2^5) = 1,200 * 2.48832 ≈ 2,986.

Therefore, the population will be approximately 2,986 butterflies five years from now.