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# 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

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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
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#1
+39
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Hold up

ReChan  May 2, 2017
#2
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So equation goes like

5000x+.04

8000x+.02

sub x with 1,2,3,etc

keep going till a passes

ReChan  May 2, 2017
#3
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And what is the value of A and B.

Guest May 2, 2017
#4
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I ain't taking away yo education XD Figure it put urself took me long enough to find out

ReChan  May 2, 2017
#5
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I'm doing Java code and I need the answer to know if my code is working and I don't know the answer so I don't know if my code is giving me the right answer.

Guest May 2, 2017
#6
+39
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Sorry dude got my own stuff to worry bout. Just use a calculator if ur lazy

ReChan  May 2, 2017
#7
+76972
+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

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