Question

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?

Answer 1

500 represents the starting number of fish.

Answer 2

`f(x) = 500(1.1)^x`

And we want to know what repreent the value 500 for this equation. If we see the general expression for an exponential function we have:

`y= ab^x`

Where a is the constant or the initial amount, b te base and x the independnet variable (time)

For this special case we know that:

`a = 500, b =1.1`

And 500 represent the constant or initial value for the function

Explanation:

We have the following function given:

`f(x) = 500(1.1)^x`

And we want to know what repreent the value 500 for this equation. If we see the general expression for an exponential function we have:

`y= ab^x`

Where a is the constant or the initial amount, b te base and x the independnet variable (time)

For this special case we know that:

`a = 500, b =1.1`

And 500 represent the constant or initial value for the function