Question

In september 1998 the population of the country of West Goma in millions was modeled by f(x) = 16.7e^0.0006x. At the same time the population of East Goma in millions was modeled by g(x) = 13.7e^0.0187x. 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.

Answer 1

you have said to estimate x when both populations are equal...
so, it is assumed that both populations are equal and written as
16.7e^0.0006x=13.7e^0.0187x
The entire equation is divided by 13.7e^0.0187x which gives,
16.7e^0.0006x/13.7e^0.0187x=1
splitting the terms
(16.7/13.7)(e^0.0006x/e^0.0187x)=1
16.7/13.7=1.21
e^0.0006x/e^0.0187x=e^-0.0181x
so we get, 1.21e^-0.0181x=1
divide the whole equation by 1.21,
e^-0.0181x=0.8264
taking natural logarithm on both sides,
-0.0181x= -0.190676361
=> x=10.53
x cannot be decimal number so approximating it to the closest integer 11
so aftr 11 yrs from 1998 population will be equal
that is at 2009 population will be equal