Question

choose the correct approximate doubling time formula for a quantity growing exponentially at a rate of p% per time period.

a. \\(t_{\text{double}} \approx 70 + p\\)
b. \\(t_{\text{double}} \approx \frac{70}{p}\\)
c. \\(t_{\text{double}} \approx \frac{p}{70}\\)
d. \\(t_{\text{double}} \approx 70 \cdot p\\)

under which conditions does the approximate doubling formula work well?

a. the approximation works best for small growth rates.
b. the approximation works best for growth rates over 100%.
c. the approximation works best for positive growth rates.
d. the approximation works best for large growth rates.

Explanation:

Identify the doubling time formula

Using the Doubling Time knowledge point

$$ T_{\text{double}} \approx \frac{70}{P} $$

Determine the conditions for the approximation

Using the Doubling Time knowledge point

$$
LATEXBLOCK0
$$

Answer:

Question 1

• A. \(T_{\text{double}} \approx 70 + P\)
• B. \(T_{\text{double}} \approx \frac{70}{P}\) (Correct answer)
• C. \(T_{\text{double}} \approx \frac{P}{70}\)
• D. \(T_{\text{double}} \approx 70 \cdot P\)

Question 2

• A. The approximation works best for small growth rates. (Correct answer)
• B. The approximation works best for growth rates over 100%.
• C. The approximation works best for positive growth rates.
• D. The approximation works best for large growth rates.