Question

Population of towns A and B increases at a rate proportional to population. In 1984, both were 20,000. In 1989, A was 25,000 and B was 28,000. The difference in 1994 was

• A. 5950
• B. 8000
• C. 7950
• D. 6950

Hint:

Population at $2t$ is $P_{0} \times (P_{t}/P_{0})^{2}$.

Answer 1

The Correct Option is C

Step 1: Concept
The growth follows $P = P_{0}e^{kt}$.

Step 2: Analysis
Town A (5 years): $25000 = 20000(e^{5k_{A}}) \implies e^{5k_{A}} = 1.25$.
Town B (5 years): $28000 = 20000(e^{5k_{B}}) \implies e^{5k_{B}} = 1.4$.

Step 3: Calculation
In 1994 ($t=10$):
$P_{A} = 20000(e^{5k_{A}})^{2} = 20000(1.25)^{2} = 31250$.
$P_{B} = 20000(e^{5k_{B}})^{2} = 20000(1.4)^{2} = 39200$.
Difference $= 39200 - 31250 = 7950$.

Step 4: Conclusion
Hence, the difference in population is 7950. Final Answer: (C)