Solve the problem.
-The population of country A in millions is modeled by $\mathrm { f } ( \mathrm { x } ) = 17.8 \mathrm { e } 0.0018 \mathrm { x }$. During the same time period, the population of country $B$ in millions is modeled by $g ( x ) = 13.7 e ^ { 0.0136 x }$. In both formulas $x$ is the number of years. Assuming these trends continue, estimate what the population will be when the populations are equal. Round to the nearest million.
A) 18 million
B) 17 million
C) 1 million
D) 19 million

Question

Quizplus · Accepted Answer

To find when the populations are equal, set $f(x) = g(x)$: $17.8e^{0.0018x} = 13.7e^{0.0136x}$. Solving for $x$ and then substituting back into either $f(x)$ or $g(x)$ will give the population when they are equal. The exact value might be complex to calculate without a calculator, but the correct answer, when rounded to the nearest million, is 19 million.

Solve the Problem f(x)=17.8e0.0018x\mathrm { f } ( \mathrm { x } ) = 17.8 \mathrm { e } 0.0018 \mathrm { x }f(x)=17.8e0.0018x

Solve the Problem $\mathrm { f } ( \mathrm { x } ) = 17.8 \mathrm { e } 0.0018 \mathrm { x }$