Question

In the month of October, the population of a species of fish in a river increased by a factor of 1.05 every day. The function below shows the number of fish in the river f(x) after x days:

f(x) = 100(1.05)x

Which of the following is a reasonable domain for the function?

0 ≤ x ≤ 100

0 ≤ x ≤ 31

All positive integers greater than 100

All positive integers less than 100

Answer 1

The reasonable domain of the function is:

0 ≤ x ≤ 31

Explanation:

In the month of October, the population of a species of fish in a river increased by a factor of 1.05 every day.

The function below shows the number of fish in the river f(x) after x days:

`f(x) = 100(1.05)^x`

We know that domain of a function is the set of all the possible value for which the function is defined.

As we know that there are 31 days in October hence, the value of x can't exceed 31.

Also at x=0 the value of f(x) represent the initial population of the fish in a river.

Hence, the domain of the function is:

0 ≤ x ≤ 31

Answer 2

In the month of October, the population of a species of fish in a river increased by a factor of 1.05 every day. The function below shows the number of fish in the river f(x) after x days:

`f(x) = 100\cdot (1.05)^x.`

The reasonable domain of the function will be the number of days of the period when the population is explored. The research take place in October, this month has 31 days, thus, the reasonable domain is

0 ≤ x ≤ 31

Answer: 0 ≤ x ≤ 31