Questions: Assume that a leader country has real GDP per capita of 80,000, whereas a follower country has real GDP per capita of 40,000. Next suppose that the growth of real GDP per capita falls to zero percent in the leader country and rises to 2 percent in the follower country. If these rates continue for long periods of time, how many years will it take for the follower country to catch up to the living standard of the leader country? Instructions: Enter your answer as a whole number. years

To determine how many years it will take for the follower country to catch up to the living standard of the leader country, we need to calculate the time it takes for the follower country's real GDP per capita to grow from \$40,000 to \$80,000 at a growth rate of 2% per year, while the leader country's real GDP per capita remains constant at \$80,000.

We can use the formula for exponential growth:

\[ P(t) = P_0 \times (1 + r)^t \]

where:

• \( P(t) \) is the future value of the GDP per capita,
• \( P_0 \) is the initial value of the GDP per capita,
• \( r \) is the growth rate (expressed as a decimal),
• \( t \) is the number of years.

In this case:

• \( P(t) = 80,000 \) (the target GDP per capita for the follower country),
• \( P_0 = 40,000 \) (the initial GDP per capita for the follower country),
• \( r = 0.02 \) (the growth rate of 2%).

We need to solve for \( t \):

\[ 80,000 = 40,000 \times (1 + 0.02)^t \]

First, divide both sides by 40,000:

\[ 2 = (1.02)^t \]

Next, take the natural logarithm (ln) of both sides to solve for \( t \):

\[ \ln(2) = \ln((1.02)^t) \]

Using the property of logarithms that \(\ln(a^b) = b \ln(a)\):

\[ \ln(2) = t \ln(1.02) \]

Now, solve for \( t \):

\[ t = \frac{\ln(2)}{\ln(1.02)} \]

Using a calculator to find the natural logarithms:

\[ \ln(2) \approx 0.6931 \] \[ \ln(1.02) \approx 0.0198 \]

So,

\[ t = \frac{0.6931}{0.0198} \approx 35 \]

Therefore, it will take approximately 35 years for the follower country to catch up to the living standard of the leader country.

The answer is: 35 years