Question

Lionfish are considered an invasive species, with an annual growth rate of 65%. A scientist estimates there are 7,000 lionfish in a certain bay after the first year.If scientists remove 1,300 fish per year from the bay after the first year, what is the recursive equation for f (n)?

Answer 1

So we know that the number of lionfish growth at a rate of 65%. This means that the number of lionfish in a certain year n without taking into account those removed by scientist is given by:

$f(n)=f(n-1)\cdot(1+\frac{65}{100})=1.65\cdot f(n-1)$

Where f(n-1) is the amount of lionfish the year prior and 1.65 represents the 65% growth. It's also important to note that scientist remove 1300 fish per year so we must substrac 1300 from that expression:

$\begin{gathered} f(n)=1.65f(n-1)-1300,\text{ }n\ge2 \\ f(1)=7000 \end{gathered}$

And that's the recursive equation for n.