Question

If the population grows at the rate of 5% per year, then the time taken for the population to become double is (Given \(\log 2 = 0.6912\))

• A. 13.624 years
• B. 13.240 years
• C. 13.725 years
• D. 13.275 years

Hint:

To find the time for population doubling, use the formula \( T = \frac{\log 2}{\log (1 + r)} \), where \( r \) is the growth rate.

Answer 1

The Correct Option is B

Step 1: Apply the doubling formula.
The time taken to double a population growing at a constant rate \( r \) is given by the formula: \[ T = \frac{\log 2}{\log (1 + r)} \] Given \( r = 0.05 \) (5%), we substitute the values: \[ T = \frac{0.6912}{\log (1.05)} \]
Step 2: Compute \( \log (1.05) \).
Using a calculator or logarithmic tables, we find: \[ \log (1.05) \approx 0.02119 \]
Step 3: Calculate the time.
Now, calculate \( T \): \[ T = \frac{0.6912}{0.02119} \approx 13.240 \text{ years} \]
Step 4: Conclusion.
Thus, the time taken for the population to double is approximately 13.240 years, which corresponds to option (B).