Question

A population has size 5000 at time t = 0, with t in years.

(a) If the population decreases by 100 people per year, find a formula for the population, P, at time t.
(b) If the population decreases by 8% per year, find a formula for the population, P, at time t.

Answer 1

The formula for the population at time t can be determined by subtracting the decrease from the initial population for (a) and using exponential decay for (b).

Step-by-step explanation:

(a) If the population decreases by 100 people per year, the formula for the population, P, at time t can be determined as:

P = 5000 - 100t

(b) If the population decreases by 8% per year, the formula for the population, P, at time t can be determined as:

P = 5000(1 - 0.08)^t