if city A's population is 5000 with a yearly growth rate of 4% and city B has a population of 8000 with a yearly growth rate of 2% when will city A surpass city B?

Guest May 2, 2017

#2**0 **

So equation goes like

5000x+.04

8000x+.02

sub x with 1,2,3,etc

keep going till a passes

ReChan
May 2, 2017

#7**+2 **

We want to solve this

5000 (1.04)^t = 8000 (1.02)^t rearrange as

(1.04)^t / (1/02)^t = 8000/ 5000

(1.04 / 1/02)^t = 8/5

(52/51)^t = 8/5 take the log of both sides

log (52/51)^t = log (8/5) and we can write

t * log (52/51) = log (8/5) divide both sides by log (52/51)

t = log (8/5) / log (52/51) = after ≈ 24.2 years

CPhill
May 2, 2017