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.
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 1,200 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

Answer:

There would be 173,535 lionfish after 6 years.

Step-by-step explanation:

Since lionfish are considered an invasive species, with an annual growth rate of 67%, ya scientist estimates there are 8,000 lionfish in a certain bay after the first year, A) to write the explicit equation for f (n) that represents the number of lionfish in the bay after n years; B) determine how many lionfish will be in the bay after 6 years; and C) if scientists remove 1,200 fish per year from the bay after the first year, determine what is the recursive equation for f (n); the following calculations must be performed:

A)

8000 x 1.67 ^ n = f  

B)

8000 x 1.67 ^ 6 = X

8000 x 21.691961596369 = X

173,535.692770952 = X  

C)

(8000 - 1200 x 1 ^ n) x 1.67 ^ n = f

Therefore, there would be 173,535 lionfish after 6 years.