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The population, P, of a species of fish is decreasing at a rate that is proportional to the population itself. If P=200000 when t=3 and P=150000 when t=4, what is the population when t=10?Round your answer to the nearest integer. Tries 0/99

The Population P Of A Species Of Fish Is Decreasing At A Rate That Is Proportional To The Population Itself If P200000 When T3 And P150000 When T4 What Is The P class=

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The Solution:

Given:

[tex]\begin{gathered} P=200,000\text{ when }t=3 \\ \\ P=150,000\text{ when }t=4 \end{gathered}[/tex]

Required:

Find P when t = 10.

Clearly, the proportion is an inverse proportion.

[tex]\begin{gathered} P=\frac{k}{t} \\ \\ Where\text{ k}=constant\text{ of proportionality.} \end{gathered}[/tex]

Applying the given values:

[tex]\begin{gathered} 200000=\frac{k}{3} \\ \\ k=3\times200,000=600,000 \end{gathered}[/tex]

This gives the formula:

[tex]P=\frac{600,000}{t}[/tex]

Substitute t=10, and find P.

[tex]P=\frac{600,000}{10}=60,000[/tex]

Answer:

The population is 60,000 when t = 10.

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