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The fish population in a local stream is decreasing at a rate of 3% per year. The original population was 48,000. Write an exponential function to model this situation. Then find the population after 7 years.

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facundobuzzetti

Answer:

Results are below.

Step-by-step explanation:

Giving the following information:

Decrease rate (d)= 7%

Number of periods (n)= 7 years

Current population (PV)= 48,000

First, to calculate the future value, we need to use the following decrease exponential formula:

FV= PV*[(1+d)^-n]

After 7 years:

FV= 48,000*(1.07^-7)

FV= 29,892

raphealnwobi

The fish population after 7 years is 38783

An exponential decay is in the form:

y = abˣ;

where y, x are variables, a is the initial value of y and b is < 1

Let y represent the fish population after x years.

Since there is initially 48000 fish, hence a = 48000. Also it decrease at a rate of 3% per year. Hence b = 100% - 3% = 97% = 0.97

Therefore:

y = 48000(0.97)ˣ

After 7 years:

y = 48000(0.97)⁷ = 38783

Therefore the fish population after 7 years is 38783

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