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:

adore.nuk
Feb 27, 2018

#1**+2 **

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

#1**+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