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.
