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. (4 points)

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. (3 points)

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. (3 points)

Answer 1

There would be 173,535 lionfish after 6 years.

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.

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