Question

use the approximate doubling time formula for the case described below. discuss whether the formula is valid for the case described.
an economic indicator is increasing at the rate of 7% per year. what is its doubling time? by what factor will the indicator increase in 5 years?

use the approximate doubling time formula. what is its doubling time?
years
(type an integer or decimal rounded to the nearest tenth as needed.)

use the approximate doubling time formula. by what factor will the indicator increase in 5 years?

(type an integer or decimal rounded to the nearest hundredth as needed.)

is this formula valid in the case described?
( ) no
( ) yes

Explanation:

Calculate the approximate doubling time

Using the Rule of 70 and Doubling Time knowledge points

$$ T_{\text{double}} \approx \frac{70}{r} = \frac{70}{7} = 10.0\text{ years} $$

Calculate the growth factor in 5 years

Using the Approximate Growth Factor knowledge point

$$ \text{Factor} = 2^{t / T_{\text{double}}} = 2^{5 / 10} = 2^{0.5} = \sqrt{2} \approx 1.41 $$

Determine the validity of the formula

Using the Rule of 70 knowledge point

$$ \text{Since } r = 7\% \text{ is a small growth rate (typically } r < 15\%\text{), the approximation is valid.} $$

Answer:

Question 1

Use the approximate doubling time formula. What is its doubling time?
<blank>10</blank> years

Question 2

Use the approximate doubling time formula. By what factor will the indicator increase in 5 years?
<blank>1.41</blank>

Question 3

Is this formula valid in the case described?

• No
• Yes (Correct answer)