In the month of September, a bird population increased by a factor of 1.25 every day for those 30 days. The function below shows the number of birds, f(x), after x days:

Question

f(x) = 250(1.25)x

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

0 ≤ x ≤ 250
0 ≤ x ≤ 30
All positive integers greater than 100
All real numbers

Answer 1

In the context of the problem, the function \( f(x) = 250(1.25)^x \) describes the growth of a bird population over a period of time, specifically for each day in September. The variable \( x \) represents the number of days.

Since the population is being tracked from day 0 to day 30 (the full month of September), the reasonable domain for the function should include days starting from 0 up to 30. Thus, the appropriate domain for \( x \) is:

\[ 0 \leq x \leq 30 \]

Therefore, the correct choice from the options provided is:

0 ≤ x ≤ 30