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ella [17]
3 years ago
6

The fish population of a lake is decreasing each year. A study is conducted. But, unfortunately some data was lost. The research

er found in her notes that in year one the fish population was 18000 fish and in year three the fish population was 8000 fish. Assume a constant rate of decay. Find a formula F
Mathematics
1 answer:
Solnce55 [7]3 years ago
4 0

Answer:

F(t) = 18000(0.6666)^{t}

Step-by-step explanation:

The fish population after t years can be modeled by the following equation:

F(t) = F(0)(1-r)^{t}

In which F(0) is the initial population and r is the constant rate of decay.

Year one the fish population was 18000

This means that F(0) = 18000

In year three the fish population was 8000 fish.

Two years later, so F(2) = 8000

F(t) = F(0)(1-r)^{t}

8000 = 18000(1-r)^{2}

(1-r)^{2} = 0.4444

\sqrt{(1-r)^{2}} = \sqrt{0.4444}

1 - r = 0.6666

r = 0.3334

So

F(t) = 18000(0.6666)^{t}

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EXPLANATION

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Since the slope is negative, there is a negative or an inverse relationship between x and y.

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See graph



Therefore, the correct answer is option D.




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