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 second option $0 \leq x \leq 31$ is the reasonable domain for f(x).

f(x) represents the population or number of a fish in the river during the month of October. So the x values should show the number of days of October. There are 31 days in October, so maximum value x should take is 31. Minimum value should be 0 which represents the population at the start of October. Therefore, the domain of f(x) will be $0 \leq x \leq 31$.

Answer 2

0 ≤ x ≤ 31 is the answer