The growth of a species of fish in a lake can be modeled by the function ƒ(x) = 500(1.10)^x , where x is time in months since January 2019. What does the 500 represent?

Question

Responses
A The number of fish after the first month.The number of fish after the first month.
B The monthly growth rate of the fish.The monthly growth rate of the fish.
C The number of fish at the end of the first year.The number of fish at the end of the first year.
D The starting number of fish in the lake.

Answer 1

The function \( f(x) = 500(1.10)^x \) represents the growth of a species of fish over time, where \( x \) is the time in months since January 2019.

In this function, the number 500 is the initial value (the value when \( x = 0 \)). This means it represents the starting number of fish in the lake when the observation begins in January 2019.

Therefore, the correct response is:

D The starting number of fish in the lake.