Final answer:
The annual growth rates needed for a country to double its output in different time frames can be estimated using the rule of 72. For 7 years, it's approximately 10.29%; for 35 years, about 2.06%; for 70 years, 1.03%; and for 140 years, 0.51%.
Step-by-step explanation:
To determine the annual growth rate needed for a country to double its output in a certain number of years, we can use the rule of 72. This rule is a simple way to estimate the number of years needed to double an investment at a given annual fixed compounded interest rate. By dividing 72 by the number of years we wish to double the output, we can find the required growth rate.
- To double in 7 years: Required growth rate = 72 / 7 ≈ 10.29%
- To double in 35 years: Required growth rate = 72 / 35 ≈ 2.06%
- To double in 70 years: Required growth rate = 72 / 70 ≈ 1.03%
- To double in 140 years: Required growth rate = 72 / 140 ≈ 0.51%
The rule of 72 provides an approximation and assumes a stable growth rate compounded annually.