Question

The population of an endangered squirrel is decreasing at a rate of 0.75% per year. There are currently

about 200,000 of these squirrels. This is represented by the equation, s = 200,000(0.9925" in which s is the
number of squirrels at any given point in time. How many squirrels will there be in 25, 50 and 100 years?

Answer 1

There will be approximately 165,689, 137,264, and 94,207 squirrels in 25, 50, and 100 years respectively.

Explanation:

Exponential Decay Function

The exponential function is often used to model natural growing or decaying processes, where the change is proportional to the actual quantity.

An exponential decaying function is expressed as:

`s(t)=s_o\cdot(1-r)^t`

Where:

s(t) is the actual value of the function at time t

so is the initial value of s at t=0

r is the decaying rate, expressed in decimal

The population of squirrels is decreasing at a rate of r=0.75% = 0.0075. The initial number of squirrels is so=200,00. The exponential model for this situation is:

`s(t)=200,000\cdot(1-0.0075)^t`

`s(t)=200,000\cdot(0.9925)^t`

Where s is the number of squirrels at any time t.

We are required to find the number of squirrels in:

t=25 years. Substitute in the formula:

`s(25)=200,000\cdot(0.9925)^25`

Calculating:

`s(25)\approx 165,689`

t=50 years. Substitute in the formula:

`s(50)=200,000\cdot(0.9925)^50`

Calculating:

`s(50)\approx 137,264`

t=100 years. Substitute in the formula:

`s(100)=200,000\cdot(0.9925)^100`

Calculating:

`s(100)\approx 94,207`

There will be approximately 165,689, 137,264, and 94,207 squirrels in 25, 50, and 100 years respectively.