Question

The population of a species of rabbit triples every year. This can be modeled by f(x) = 4(3)x and f(5) = 972. What does the 972 represent

Answer 1

972 represents the population of the rabbits after five years.

Explanation:

We are given that the population of a species of rabbit triples every year. This can be modeled by f(x) = 4(3)x and f(5) = 972.

We know that the exponential growth function is given by:

`f(x)=Ab^x`

where
`x` represents the numbers of years.

Therefore, 5 in f(5) represents the year and thus, 972 represents the population of the rabbits after five years.

Answer 2

972 is the population of rabbits in the year 5

Explanation:

`f(x) = 4(3)^x` is an increasing exponential function of base 3. The fact that its base is 3 means that the function triples when x increases one unit.

It is said that the population triples every year. Therefore x represents the number of years elapsed and f(x) represents the number of rabbits in year x

If f(x) represents the population of rabbits for the year x, then, f(5) represents the population of rabbits for x = 5, that is to say, after having passed 5 years.

So, 972 is the population of rabbits in the year x = 5