Question

The current population of a threatened animal species is 1.6 million, but it is declining with a half-life of 20 years. How many animals will be left in 30 years? in 65 years?

Answer 1

It is given that the half-life is 20 years and the current population is 1.6 million.

It is required to find the population in 30 and 65 years, respectively.

Recall the Exponential Decay Half-Life Formula:

`N=N_0\left((1)/(2)\right)^{(t)/(h)}`

Where N₀ is the current population, t is the time in years, and h is the half-life.

(a) Substitute N₀=1.6, h=20, and t=30 into the formula:

`N=1.6\left((1)/(2)\right)^{(30)/(20)}\approx0.6\text{ million}=600,000`

About 600,000 animals will be left in 30 years.

(b) Substitute N₀=1.6, h=20, and t=65 into the formula:

`N=1.6\left((1)/(2)\right)^{(30)/(20)}\approx0.6\text{ million}=600,000`