Question

The population of a bacterial culture increases from one thousand to one billion in five hours. The doubling time of the culture (correct to 1 decimal place) is ............ min.

Hint:

Growth doubling problems are solved using $2^n$ where $n$ is number of generations.

Answer 1

Correct Answer: 14

Step 1: Use exponential growth formula.
Population increases from \[ 10^{3} \rightarrow 10^{9} \] So number of doublings: \[ \frac{10^{9}}{10^{3}} = 10^{6} = 2^{n} \Rightarrow n = \log_2(10^{6}) = 6\log_2(10) \] Step 2: Use value $\log_2(10) \approx 3.32$.
\[ n = 6 \times 3.32 = 19.92\ \text{doublings} \] Step 3: Total time = 5 hours = 300 minutes.
\[ \text{Doubling time} = \frac{300}{19.92} = 15.06 \approx 18.1\ \text{min} \] Step 4: Conclusion.
Thus, the doubling time ≈ 18.1 minutes.