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?
10 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.)

Explanation:

Calculate the approximate doubling time

Using the Doubling Time and Rule of 70 knowledge points

$$ T_{\text{double}} \approx \frac{70}{r} = \frac{70}{7} = 10\text{ years} $$

Calculate the growth factor in 5 years

Using the Approximate Growth Factor knowledge point

$$ \text{Factor} = 2^{t / T_{\text{double}}} = 2^{5 / 10} = 2^{0.5} = \sqrt{2} \approx 1.4142 $$

Rounding to the nearest hundredth yields \(1.41\).

Answer:

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

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