A few days ago
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Economics question?

Richland’s real GDP per person is $10,000, and Poorland’s real GDP per person is $5,000. However, Richland’s real GDP per person is growing at 1 percent per year and Poorland’s is growing at 3 percent per year. Compare real GDP per person in the two countries after 10 years and after 20 years. Approximately how many years will it take Poorland to catch up to Richland?

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A few days ago
math guy

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Richland GDP/ person in 1 year = $10,000*1.01 = $10,100

in 3 years = $10,000*(1.01^3) = $10,303.01

in 5 years = $10,000*(1.01^5) = $10,510.10

Poorland’s GDP/person in 1 year = $5,000*1.03 = $5,150

in 3 years = $5,000*(1.03^3) = $5,463.64

in 5 years = $5,000*(1.03^5) = $5,796.37

To catch up,

10,000*(1.01^x) = 5000(1.03^x)

2 = (1.03^x)/(1.01^x)

2 = (1.03/1.01)^x

log 2 = log(1.03/1.01) * x

log 2 / log(1.03/1.01) = x

x = approx 35.3 years

At that time, both would have a GDP/person of $14,215.36.

I hope this helps!

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