Question

Park rangers released 4 fish into a pond in year 0. Each year, there were 3 times as many fish as the year before. Write a function to represent this scenario.

Answer 1

The function representing the scenario where 4 fish multiply by a factor of 3 each year is f(n) = 4 × 3^n, where n is the number of years since the initial release.

Step-by-step explanation:

To write a function to represent the scenario where park rangers released 4 fish into a pond in year 0, and each year there are 3 times as many fish as the year before, we use an exponential growth model. Let n represent the number of years since the initial release and f(n) represent the number of fish at year n.

The function can be written as:

f(n) = 4 × 3^n

Here, the initial number of fish is the starting value, which is 4, and the base of the exponent, 3, represents the growth factor each year (the number of times the fish population increases each year).

For example, to find the number of fish after 1 year, we substitute n with 1:

f(1) = 4 × 3^1 = 4 × 3 = 12 fish