Question

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

• A. 13.8275 years
• B. 13.624 years
• C. 13.725 years
• D. 13.8240 years

Hint:

For exponential growth problems, doubling time is found by equating the growth factor to 2 and using logarithms to solve for time.

Answer 1

The Correct Option is D

Step 1: Write the growth formula.
For population growth, \[ P = P_0 (1+r)^t \] Here, \( r = 0.05 \) and the population becomes double, so \[ 2P_0 = P_0 (1.05)^t \] Step 2: Simplify the equation.
\[ 2 = (1.05)^t \] Taking logarithm on both sides, \[ \log 2 = t \log(1.05) \] Step 3: Substitute given values.
Using \( \log 2 = 0.6912 \) and \( \log(1.05) \approx 0.0217 \), \[ t = \frac{0.6912}{0.0217} \] Step 4: Calculate the time.
\[ t \approx 13.8240 \text{ years} \]