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? (1 point)

0 ≤ x ≤ 100

0 ≤ x ≤ 31

All positive integers greater than 100

All positive integers less than 100

The function \( f(x) = 100(1.05)^x \) represents the population of a species of fish after \( x \) days in the month of October. Since October has 31 days, the domain should represent the number of days within October.

- \( x \) represents the number of days, starting from 0 (which would be the beginning of October) up to 31 days.

So, the reasonable domain for the function is:

\[ 0 \leq x \leq 31 \]

This means the correct answer is:

**0 ≤ x ≤ 31**

Would you like more details or have any questions? Here are some related questions:

1. What would the population of the fish be after 10 days?
2. How does the factor of 1.05 affect the fish population growth?
3. What is the population at the beginning of the month (when \( x = 0 \))?
4. How would the function change if the growth factor were different, say 1.02?
5. What would happen to the population if \( x \) were beyond 31 days?

**Tip:** Exponential functions like this one model situations where something grows by a constant percentage over equal time intervals.

Explore how exponential growth applies to a fish population in a river over the course of October. Learn about the function f(x) = 100(1.05)^x and its domain, which represents the number of days in October. Suitable for Grades 7-9.

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