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.

Part A: Write the explicit equation for f (n) that represents the number of lionfish in the bay after n years. Show all necessary math work.

Part B: How many lionfish will be in the bay after 6 years? Round to the nearest whole number and show all necessary math work.

Part C: If scientists remove 1,300 fish per year from the bay after the first year, what is the recursive equation for f (n)? Show all necessary math work.

Answer 1

Part A: The explicit equation for f(n) representing the number of lionfish after n years with a 65% annual growth rate can be calculated using the formula:

\[f(n) = 7,000 \times (1 + 0.65)^n\]

Part B: To find the number of lionfish after 6 years, substitute n = 6 into the equation:

\[f(6) = 7,000 \times (1 + 0.65)^6\]

Calculate this expression to find the result.

Part C: For the recursive equation, you subtract 1,300 lionfish per year from the previous year's total. The recursive equation is:

\[f(n) = f(n-1) - 1,300\]

These equations capture the growth and removal dynamics of the lionfish population over time.