Question

Richland's Real GDP per person is #10b and poorland's Real GDP per person is #5b. However, Richland's Real GDP per person is growing at 1% per year and poorland's Real GDP per person is growing at 3% per year. Compare real GDP per person in the two countries after ten years and after twenty years. Approximately how many years will it take poorland to catch up with Richland?

Answer 1

• after 5 years, rich : poor = 11.0 : 6.7
• after 10 years, 12.2 : 9.0
• 35.3 years

Explanation:

It is convenient to let a graphing calculator show the answers to these questions.

The exponential equation modelling the growth will be of the form ...

f(x) = (initial value) × (1 +growth rate)^x

Richland's GDP/person can be modeled by r(x) = 10·1.01^x

Poorland's GCP/person can be modeled by p(x) = 5·1.03^x

The attached graph shows values for x=5, 10 and r(x)=p(x).

It will take about 35.3 years for Poorland to catch up.