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# if city A's population is 5000 with a yearly growth....

+1
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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?

City A13329.182
City B 13124.849
25 years

???

Guest May 2, 2017
#1
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City A: 125000.04

City B: 200000.02

Just saying this is 25 yrs.

ReChan  May 2, 2017
edited by ReChan  May 2, 2017
#2
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that is way too much for 25 years

Guest May 2, 2017
#3
+39
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Lemmie recheck

ReChan  May 2, 2017
#4
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Ah yes I did do a mistake

Town A: 10000

Town B: 12000

ReChan  May 2, 2017
#5
-2

You're terrible at math

Guest May 2, 2017
#6
+17746
+2

City A:  population = 5000(1.04)n

City B:  population = 8000(1.02)n

These will be equal when:  5000(1.04)n  =  8000(1.02)n

Find the log of both sides:      log( 5000(1.04)n )  =  log( 8000(1.02)n )

Rewriting:                      log( 5000 ) + log( 1.04n )  =  log( 8000 ) + log( 1.02n )

Rewriting:                   log( 5000 ) + n · log( 1.04 )  =  log( 8000 ) + n · log( 1.02 )

Rearranging:        n · log( 1.04 )  -  n · log( 1.02 )  =  log( 8000 ) - log( 5000 )

Factoring:                   n ( log( 1.04 ) - log( 1.02 ) )  =  log( 8000 ) - log( 5000 )

Dividing:               n  =  [ log( 8000 ) - log( 5000 ) ]  /  [  log( 1.04 ) - log( 1.02 ) ]

Using a calculator, n = 25.

Also:  5000(1.04)25  =  13329

8000(1.02)25  =  13125

geno3141  May 2, 2017