If the GDP of country X is 4 times the GDP of country Y and if the GDP of country X remains constant while GDP of country Y grows at a rate of 7% per year,which of the following statements is true?

Question

Quizplus · Accepted Answer

To determine when Country Y's GDP will equal Country X's GDP, we can use the formula for exponential growth: $Y(t) = Y_0(1 + r)^t$, where $Y(t)$ is the GDP of Country Y at time $t$, $Y_0$ is the initial GDP of Country Y, $r$ is the growth rate (7% or 0.07), and $t$ is the time in years. Since Country X's GDP is 4 times Country Y's initial GDP ($X = 4Y_0$), we want to find $t$ when $4Y_0 = Y_0(1 + 0.07)^t$. Simplifying, we get $4 = (1.07)^t$. Solving for $t$ (using logarithms or trial and error), we find that $t$ is approximately 20 years, meaning it will take about 20 years for Country Y's GDP to equal Country X's GDP, assuming a constant 7% annual growth rate for Country Y and no growth for Country X.

If the GDP of Country X Is 4 Times the GDP