In September 1998 the population of the country of West Goma in millions was modeled by $f ( x ) = 17.5 e ^ { 0.0010 x }$. At the same time the population of East Goma in millions was modeled by $\mathrm { g } ( \mathrm { x } ) = 13.7 \mathrm { e } 0.0129 \mathrm { x }$. In both formulas $x$ is the year, where $x = 0$ corresponds to September 1998 . Assuming these trends continue, estimate the year when the population of West Goma will equal the population of East Goma.
A) 21
B) 1977
C) 2019
D) 2016

Question

Quizplus · Accepted Answer

To find when the populations are equal, set $f(x) = g(x)$: $17.5 e^{0.0010x} = 13.7 e^{0.0129x}$. Solving for $x$, we get $x \approx 21$. Since $x = 0$ corresponds to 1998, the year is 1998 + 21 = 2019.

In September 1998 the Population of the Country of West f(x)=17.5e0.0010xf ( x ) = 17.5 e ^ { 0.0010 x }f(x)=17.5e0.0010x

In September 1998 the Population of the Country of West $f ( x ) = 17.5 e ^ { 0.0010 x }$