Question

Imagine a population of birds with an initial size of 100, a per-capita birth rate of 2, and a per-capita death rate of 1 per year. Use the discrete time form of the exponential growth equation to predict the number of individuals in this population after 5 years of growth.

Answer 1

3200

Explanation:

Given that:

The initial population of birds
`N_0` = 100

The time duration t = 5 years

Growth rate (r) = (Birth - Death) rate

= 2 - 1

= 1 / year

∴

using the discrete-time form:

`N_t = N_o (1 + r )^t`

`N_t = 100 (1 + 1 )^5`

`N_t = 100 (2 )^5`

`N_t = 100 * 32`

`N_t = 3200`