Question

. City workers recorded the number of squirrels in a park over a period of time. At the first count, there were 15 pairs

of male and female squirrels (30 squirrels total). After 6 months, the city workers recorded a total of 60 squirrels,
and after a year, there were 120.
a. What type of function can best model the population of squirrels recorded over a period of time, assuming the
same growth rate and that no squirrel dies?
b. Write a function that represents the population of squirrels recorded over xx number of years. Explain how you determine your function.

Answer 1

Exponential

P(X) = P_0 (2)^{2x}

Explanation:

Given that at the first count, there were 15 pairs

of male and female squirrels (30 squirrels total). After 6 months, the city workers recorded a total of 60 squirrels,

and after a year, there were 120.

i.e. every 6 months population of squirrel is doubling.

a) Function is exponential since every time of 6 months population is doubled

b) The function that represents the population of squirrels recorded over x number of years.

We know that every 1/2 year it doubles. Hence initially if P0 is started with in 1/2 year it would be 2P0 and in 1 year it would be 4P0 and so on.

In other words, the model would be

`P(X) = P_0 (2)^(2x)` where x = no of years