A mathematical approximation called the rule of 70 tells us how long it will take for something to double in size if it grows at a constant rate. The doubling time is approximately equal to the number 70 divided by the percentage rate of growth. Thus, if Oman's real GDP per person is growing at 7 percent per year, it will take about 10 years (= 70 ÷ 7) to double. Apply the rule of 70 to solve the following problem: Real GDP per person in Oman in 2020 was about $15,000 per person, while it was about $60,000 per person in the United States. If real GDP per person in Oman grows at the rate of 10 percent per year, about how long will it take Oman's real GDP per person to reach the level that the United States enjoyed in 2020? (Hint: How many times would Oman's 2020 real GDP per person have to double to reach the United States' 2020 real GDP per person?)

Respuesta :

Answer:

  14 years

Step-by-step explanation:

You want to know the time it takes for a GDP of $15,000 per person to grow to $60,000 per person at the rate of 10% per year.

Doublings

If the GDP doubles, it will be $30,000 after about 70/10 = 7 years.

If it doubles again, it will be $60,000 after 7 more years.

The GDP will be about $60,000 per person after 14 years.

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Additional comment

A more exact calculation gives the time as 14.5 years, so the approximation has an error of less than 4%.