Question

A scientist studies a population of squirrels in a certain region for several years. There are initially 24 squirrels and the squirrel population doubles every year.

Which function best represents the number of squirrels in the region at the end of x years? Justify your answer.

Answer 1

If the squirrel population doubles every year, then we can represent the number of squirrels at the end of x years as:

f(x) = 24 x 2^x

where f(x) is the number of squirrels at the end of x years.

To see why this is the correct function, we can examine what happens to the squirrel population each year.

After one year, the squirrel population doubles to 24 x 2 = 48 squirrels.

After two years, the squirrel population doubles again to 24 x 2^2 = 96 squirrels.

After three years, the squirrel population doubles again to 24 x 2^3 = 192 squirrels.

We can see that the number of squirrels at the end of each year is double the number from the previous year. This exponential growth can be represented by the function f(x) = 24 x 2^x.

Therefore, the function that best represents the number of squirrels in the region at the end of x years is f(x) = 24 x 2^x.