Question

in 2010, the population of a town is 8500. the population decreases by 4.5% each year. write an equation to find the population of the town t years after 2010. in what year will the population of the town be 7000.

Answer 1

P(t) = 8500(1 - 0.045)^t - base equation

7000 = 8500(1 - 0.045)^t
0.8235 = (0.955)^t
ln 0.8235 = ln 0.955^t
ln 0.8235 = t ln 0.955
(ln 0.8235)/(ln 0.955) = t
t = 4.216 years

Answer 2

in 2014

Explanation:

Given that in 2010, the population of a town is 8500. the population decreases by 4.5% each year.

Hence equation for population would be

`P(t) = 8500(0.955)^t`

It is required to find out the year in which the population will be 7000.

`P(t) = 8500(0.955)^t=7000\\0.955^t =(7000)/(8500) =0.8235\\`

Take log to get

t log 0.955 = log 0.8235

t=
`(-0.08432)/(-0.0199)`

=4.237 year

i.. in 2014 year the population will become 7000