Question

Lionfish are considered an invasive species, with an annual growth rate of 67%. A scientist estimates there are 8,000 lionfish in a certain bay after the first year.Write the explicit equation for f(n) that represents the number of lionfish in the bay after n years.

Answer 1

f(n) = 8000(1.67)ⁿ⁻¹

Step-by-step explanation:

The equation for exponential growth has the following form:

`f(x)=a(1+r)^x`

Where a is the initial amount, r is the growth rate and x is the variable.

In this case, we know the amount after the first year and the growth rate and the variable is the number of years. So, replacing a by 8,000 and r by 0.67 and x by (n-1) because we will not include the 1st year, we get:

`f(n)=8000(1+0.67)^(n-1)`

Therefore, the explicit equation for f(n) is:

`f(n)=8000(1.67)^(n-1)`