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2. In 2010, the population of a town is 8500. The population decreases by 4.5% each year.

(a) Write an equation to find the population of the town t years after 2010.

(b) In what year will the population of the town be 7000? Show your work.

 

Answer:

 Feb 27, 2018

Best Answer 

 #1
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Current population =P(c)

Future population  =F(p)

F(p) = P(c) x [1 - 0.045]^t

F(p) = P(c) x [0.955]^t

7,000 = 8,500 x [0.955]^t     divide both sides by 8,500

0.823529... = 0.955^t           take the log of both sides

t = log(0.823529) / log(0.955)

t = ~ 4.217 years - when the population of the town will be about 7,000.

So, it will be: 2010 + 4.217 =~2014

 Feb 27, 2018
edited by Guest  Feb 27, 2018
 #1
avatar
+2
Best Answer

Current population =P(c)

Future population  =F(p)

F(p) = P(c) x [1 - 0.045]^t

F(p) = P(c) x [0.955]^t

7,000 = 8,500 x [0.955]^t     divide both sides by 8,500

0.823529... = 0.955^t           take the log of both sides

t = log(0.823529) / log(0.955)

t = ~ 4.217 years - when the population of the town will be about 7,000.

So, it will be: 2010 + 4.217 =~2014

Guest Feb 27, 2018
edited by Guest  Feb 27, 2018
 #2
avatar+587 
+1

thank you so much!

adore.nuk  Feb 27, 2018

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