Knowee
Questions
Features
Study Tools

The rule of 72 gives the approximate doubling time of a variable if you know its rate of growth. For example, if the population of a country is 200 million and the rate of growth of its population is 2 percent per year, then it will take approximately 36 years for the country’s population to reach 400 million.Assume that per capita income in 2006 was $40,000 in the United States and $5,000 in China. If the per capita income growth rate in China is 9 percent a year, how long will it take for China to reach a per capita income level that is equivalent to the United States’ 2006 per capita income level?

Question

The rule of 72 gives the approximate doubling time of a variable if you know its rate of growth. For example, if the population of a country is 200 million and the rate of growth of its population is 2 percent per year, then it will take approximately 36 years for the country’s population to reach 400 million.Assume that per capita income in 2006 was 40,000intheUnitedStatesand40,000 in the United States and 5,000 in China. If the per capita income growth rate in China is 9 percent a year, how long will it take for China to reach a per capita income level that is equivalent to the United States’ 2006 per capita income level?

...expand
🧐 Not the exact question you are looking for?Go ask a question

Solution

To calculate the time it will take for China to reach the same per capita income level as the United States in 2006, we can use the rule of 72. This rule states that if you divide 72 by the annual growth rate, you will get the approximate number of years it will take for a variable to double.

In this case, the per capita income in China in 2006 was $5,000 and the growth rate is 9 percent.

Step 1: Calculate the number of times the income needs to double to reach the target. The target is 40,000andthestartingpointis40,000 and the starting point is 5,000. So, 40,000/40,000/5,000 = 8. This means the income needs to double 3 times because 2^3 = 8.

Step 2: Calculate the doubling time. Using the rule of 72, the doubling time is 72/9 = 8 years.

Step 3: Multiply the number of doublings by the doubling time. So, 3 doublings * 8 years/doubling = 24 years.

Therefore, it will take approximately 24 years for China to reach a per capita income level that is equivalent to the United States’ 2006 per capita income level, assuming a constant growth rate of 9 percent.

This problem has been solved

Similar Questions

The per capita income of a developing country is $10,000, while that of an industrialized country is $40,000. If the developing country's income per capita grows at 6% per year while the industrialized income per capita grows at 3%, approximately how long will it take for the developing country's income per capita to equal that of the industrialized country's (rounded to the nearest tenth of a year)?It would take  years for the two countries' per capita incomes to equal each other.

In a developing country, the growth rate of capital is 6% per hour of work, and the growth rate of technology is 3%. How many years will it take the developing country's per capita income to double (rounded to the nearest tenth of a year)? It will take the country's per capita income approximately  years to double.

India has a population of 1 billion and current population growth is 1.9 %, what is the doubling time?a.37 yearsb.15 yearsc.10 yearsd.100 years

If an economy is growing at a rate of 3.5% per year, how long will it take the economy to double in size? Choose the closest answer. 70 years 35 years 43 years 20 years 36 years

The following are GDP figures for Country A Year GDP (bn) 2022 $212 2021 $200 If Country A maintains the same growth rate, how long will it take for GDP to reach $424bn?

1/3

Upgrade your grade with Knowee

Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.