Problema Solution
In September 1998 the population of the country of West Goma in millions was modeled by f(x)=17.8e^0.0014x. At the same time the population of East Goma in millions was modeled by g(x)=13.4e^0.0116x. 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.
Answer provided by our tutors
the populations are equal for x, x>0 means:
f(x) = g(x)
17.8e^0.0014x = 13.4e^0.0116x
e^0.0014x = (13.4/17.8)e^0.0116x
0.0014x = 0.0116x + ln(13.4/17.8)
x = (-1/0.0102)*ln(13.4/17.8)
x = 27.84
f(27.84) = 17.8e^(0.0014*27.84)
e = 2.718282
f(27.84) =
f(x) = 17.8*(2.718281)^(0.0014*27.84)
f(x) = 18.51 millions
when the populations are equal there are 18.51 millions in each country.