Question

a population of insects increases at a rate of 1.5% per day. about how long will it take the population to double?

2.5 days
5.0 days
46.6 days
66.7 days

Explanation:

Set up the exponential growth equation

Using the Exponential Growth Calculation knowledge point

$$ P(t) = P_0(1 + r)^t $$

$$ 2P_0 = P_0(1 + 0.015)^t $$

Solve for the doubling time

Using the Doubling Time Model knowledge point

$$ 2 = (1.015)^t $$

$$ t = \frac{\ln(2)}{\ln(1.015)} $$

$$ t \approx \frac{0.693147}{0.014889} \approx 46.56 $$

Match with the closest option

$$ t \approx 46.6\text{ days} $$

Answer:

• 2.5 days
• 5.0 days
• 46.6 days (Correct answer)
• 66.7 days