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consider the following data: Country population real GP A 10 55 billion B 20 60

ID: 1177130 • Letter: C

Question

consider the following data:

Country                population            real GP

A                          10                          55 billion

B                           20                        60 billion

C                             5                         70 billion

What is the per capita real GDP in each of these countries?

Per capita in country L is three times as high as in country M. Th economic growth rate in country M is 8 percent while country L's economy grows at a rate of 5 percent.

How many years will it be before per capita GDP in counry M surpasses per capita real GDP in country L?

Explanation / Answer

Part 2:

Let X be the per capita GDP of country L and let this be year 0. Then:
X(n) = X(0) (1 + 0.05)^n
Let Y be the per capita GDP of country M, then

Y(n) = Y(0) (1.0.08)^n
You are given that X(0) = 3 * Y(0) and are asked to find n such that X(n) = Y(n)
So you know:
3 * Y(0) (1 + 0.05)^n = Y(0) (1 + 0.08)^n

Divide both sides by Y(0) and you have a simple equation in one unknown: n.
3 * (1 + 0.05)^n = (1 + 0.08)^n
or
3 = [(1 + 0.08) / (1 + 0.05)]^n

Log 3 = n Log R
0.478=n0.012

0.478/0.012=n

n =38.83