Question

If the population grows at the rate of \( 8% \) per year, then the time taken for the population to be doubled is \([ \log 2 = 0.6912 ]\)

• A. \( 8.64 \) years
• B. \( 6.8 \) years
• C. \( 10.27 \) years
• D. \( 4.3 \) years

Hint:

For population growth problems, doubling time is found using \[ t = \frac{\log 2}{r} \] where \( r \) is the rate of growth.

Answer 1

The Correct Option is A

Step 1: Use the exponential growth formula.
Population growth is given by \[ P = P_0 e^{rt} \] Step 2: Apply the condition for doubling.
\[ 2P_0 = P_0 e^{0.08t} \] \[ 2 = e^{0.08t} \] Step 3: Take logarithm on both sides.
\[ \log 2 = 0.08t \] Step 4: Substitute the given value.
\[ 0.6912 = 0.08t \] Step 5: Solve for \( t \).
\[ t = \frac{0.6912}{0.08} = 8.64 \] Step 6: Conclusion.
The time taken for the population to double is \( 8.64 \) years.