Question

The population increases from \(40000\) to \(80000\) in \(20\) years, then the population in another \(40\) years will be

• A. \(240000\)
• B. \(160000\)
• C. \(320000\)
• D. \(640000\)

Hint:

If a quantity doubles every fixed interval, then after \(n\) such intervals it becomes: \[ \text{Initial value} \times 2^n \]

Answer 1

The Correct Option is C

Step 1: Understanding the Concept:
Exponential growth follows \(P = P_0 e^{kt}\).
Step 2: Key Formula or Approach:
Population doubles in \(20\) years.
Step 3: Detailed Explanation:
In \(20\) years: \(80k = 40k(e^{20k}) \implies e^{20k} = 2\).
Total time after start is \(20 + 40 = 60\) years.
\(P(60) = 40k(e^{20k})^3 = 40k(2)^3 = 320,000\).
Step 4: Final Answer:
Population is \(320,000\).