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

Concept:
If the population doubles in a fixed time interval, then exponential growth is implied. Here, the population doubles from \(40000\) to \(80000\) in \(20\) years. ip

Step 1: Find the growth pattern.
Given: \[ 40000 \to 80000 \] in \(20\) years. So the population doubles every \(20\) years. ip

Step 2: Find the number of doubling periods in the next \(40\) years.
Another \(40\) years means: \[ \frac{40}{20}=2 \] more doubling periods. ip

Step 3: Calculate the population after \(40\) more years.
Starting from \(80000\), \[ 80000 \times 2^2 = 80000 \times 4 = 320000 \] ip Hence, the correct answer is:
\[ \boxed{(C)\ 320000} \]