a.
To state: A recursive rule for the number of fish at the beginning of the nth year and the number of fish at the beginning of the 5th year if a lake initially contains 5000 fish.
The resultant fish are 3524.
Given information:
A lake initially contains 5000 fish. Each year the population declines 20% due to fishing and other causes, and the lake is restocked with 500 fish.
Explanation:
Consider the given information,
A lake initially contains 5000 fish. It means
Each year the population declines 20% due to fishing and other causes, and the lake is restocked with 500 fish.
Thus, the recursive rule is
The second term is:
The third term is:
The fourth term is:
The fifth term is:
Therefore, at the beginning of 5th year there will be 3524 fish in the lake.
b.
To state: What happens to the population of fish in the lake over time.
The fish in the lake will disappear over time.
Given information:
A lake initially contains 5000 fish.
Explanation:
A lake initially contains 5000 fish.
Each year the population declines 20% due to fishing and other causes, and the lake is restocked with 500 fish.
The lake contains 5000 fish in it. After a year, it reduced to 4500 fish. Then after two years the number of fish reduced to 4100. Then again it reduced to 3780, 3524 and so on.
This pattern will continue for a long time. It can be seen that the number of fish in the lake is decreasing and over time the fish in lake will disappear.
Chapter 7 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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