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http://prntscr.com/litfal

 Nov 15, 2018
 #1
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+1

Future Population=FP
Present Population=PP
FP = PP x [1 + (-0.045)]^t - Town's population t years after 2010
7,000 = 8,500 x [1 - 0.045]^t
7,000 = 8,500 x       0.955^t    Divide both sides by 8,500
0.8235294 = 0.955^t                Take the log of both sides
t =Log(0.8235294) / Log(0.955)
t =4.22 =~4 years after 2010.

 Nov 15, 2018
 #2
avatar+106515 
+1

a)     P  = 8500 ( 1 - .045)^t

 

Where  P   is the population  "t" years after 2010

 

b)   7000 =   8500 ( 1 - .045)^t

Divide both sides by 8500

 

7000/8500 =  ( 1 - .045)^t

Take the log of both sides

 

log (700/8500)  =  log ( 1 -.045)^t

And by a log property we can write

 

log ( 7000/8500) = t * log (1 - .045)

Divide both sides by  log ( 1 - .045)

 

t  =   log ( 7000/8500) / log (1 - .045) ≈  4.2 years

 

So....the population will be 7000  in about  2014

 

 

cool cool cool

 Nov 15, 2018

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