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?
(a) 0 ≤ x ≤ 100
(b) 0 ≤ x ≤ 31
(c)- All positive integers greater than 100.
(d)-All positive integers less than 100

Answer 1

(a) 0 ≤ x ≤ 100

Explanation:

Answer 2

The correct choice for a reasonable domain for the function is option (b) 0 ≤ x ≤ 31.

How to determine the reasonable domain for the function

To determine the reasonable domain for the function f(x) = 100(1.05)x

Given that the function represents the number of fish in the river after x days in the month of October, we can reasonably assume that the maximum number of days in October is 31.

Therefore, option (b) 0 ≤ x ≤ 31 is a reasonable domain for the function.

In this case, x represents the number of days in October, and it ranges from 0 to 31 because the population is being tracked and modeled specifically for the month of October.

Therefore, the correct choice for a reasonable domain for the function is option (b) 0 ≤ x ≤ 31.