Question

The number of citizens in a town is growing according to a linear growth model. The initial population in week 0 was P_0=124 and the population after 18 months is P_(18 )=184. Write an explicit formula for the number of citizens in the town depending on the month.
After how many months will the population reach 1000?

Answer 1

184 - 124 = 60
so it has grown  by 60 in 18 months. That is 3 1/3 per month.

so Number of citizens depending on month  is 124 + (1 1/3)n
or 124 + 4n/3:

At population 1000:-
124 + 4n/3  = 1000
4n/3 = 1000-124

n  =  (1000-124) * 3/4  =  657 months