Question

Scientist released 5 foxes into a new habitat in year 0. Each year, there were four times as many foxes as the year before. How many foxes were there after x years? Write a function to represent this scenario

Answer 1

The function that this scenario represents is:

`P(x) = 5(4) ^ x`

Explanation:

The initial number of foxes was 5. The following year they had

year 1:
`5 * (4) = 20` foxes

year 2:
`5 * 4 * (4) = 80` foxes

year 3:
`5 * 4 * 4 * (4) = 320` foxes

year x:
`5 * 4 ^ x` foxes

Then the equation that models the situation is an equation of exponential growth. Where P(x) is the population of foxes in year x.

So:

`P(x) = 5(4) ^ x`