There is a state that has 3 cities: City A, City B and City C.
In 1910 both had 2000 inhabitants. City C grew for a time, but by 1915 it was zero. In contrast, City B had exponential growth. In 2011 both had 6000 stable inhabitants.
The population of one of the cities can be modeled with the function f (x) = k · (a ^ x) and the other, with the function g (x) = - (x ^ 2) + b * x + c ( x indicates the time in years; and represents -in thousands- the number of inhabitants).
a) Determine which function corresponds to the number of inhabitants of each city and obtain the values of a, b, c and k. b)
b) Find the equation of a function that models the number of inhabitants of City A, knowing that its population grew at a rate of 1500 inhabitants per year.
c) Determine when City A and City C had the same number of inhabitants