+525 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:
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
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
