population growth word problem please help

Question

The population of the GTA is growing at 12 % per year. If the population of Toronto is 2.9 million in 2020, how many people would we expect to have by 2045?

1. Write an equation to model the population growth P(t), from 2020, t.
2. Use your equation to find how many people will be in the GTA in 2045

Answer 1

P(x) = Ae^rt

P(t) = 2.9e^.12t where t = years after 2020, .12 = 12% annual interest compounded continuously. 2.9 = units of one million

P(25) = 2.9e^.12(25) where t=25 means 2020+25= 2045

= 2.9e^3

=about 2.9(20.08553692)

=58.24805708

= 58,248,057 population in year 2045

= almost 58 1/4 million

or if you want just annual compounding the formula is

P(t) = A(1+r)^t

P(25) = 2.9(1+0.12)^25

= 2.9(1.12)^25

=49,3 million by 2045