Solve the problem.
-In September 1998 the population of the country of West Goma in millions was modeled by $f ( x ) = 17.8 e ^ { 0.0018 x }$. At the same time the population of East Goma in millions was modeled by $g ( x ) = 13.1 e ^ { 0.0148 x }$. In both formulas $x$ is the year, where $x = 0$ corresponds to September 1998. Assuming these trends continue, estimate what the population will be when the populations are equal.
A) 1 million
B) 17 million
C) 19 million
D) 18 million

Question

Quizplus · Accepted Answer

To find when the populations are equal, set $f(x) = g(x)$: $17.8e^{0.0018x} = 13.1e^{0.0148x}$. Solving for $x$ involves logarithms and algebra, but the question asks for the population, not the year. By equating the two functions and solving, we find the point where their populations are the same. Without the exact calculations here, we know the answer involves finding the population at that point, which is estimated to be around 19 million based on the growth rates and initial populations given.

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

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