151k views
4 votes
Lionfish are an invasive species, with an annual growth rate of 69%. A scientist guesses there are 9,000 lionfish in a body of water 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 WORK.

Part B: How many lionfish will be in the bay after 6 years? SHOW ALL WORK AND ROUND TO NEAREST WHOLE NUMBER.

Part C: If scientists remove 1,400 fish per year from the bay after the first year, what is the recursive equation for f(n)? SHOW ALL WORK.

1 Answer

2 votes

Answer & Step-by-step explanation:

Part A: The explicit equation for f(n) that represents the number of lionfish in the bay after n years can be written as:

f(n) = 9000 * (1 + 0.69)^n

where 9000 is the initial number of lionfish, 0.69 is the growth rate, and n is the number of years.

Part B: To find the number of lionfish in the bay after 6 years, we substitute n = 6 into the explicit formula from Part A and simplify:

f(6) = 9000 * (1 + 0.69)^6 = 9000 * (1.69)^6 = 9000 * 11.34 = 102,060.5

Rounding to the nearest whole number, there will be approximately 102,061 lionfish in the bay after 6 years.

Part C: The recursive equation for f(n) can be found by subtracting 1,400 from the previous year's population and then applying the annual growth rate. Thus, we have:

f(1) = 9000 f(n) = f(n-1) - 1400 + 0.69f(n-1) = 0.69f(n-1) - 1400

where f(1) is the initial number of lionfish and n represents the number of years after the first year.

User Thenoseman
by
8.0k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories