Question

In 2010, a city population was 55,210 and it was declining at a rate of 1.09 each year. What is the best prediction for when the city population will first be below 48,000?

2019
2022
2025
2028

Answer 1

48000=55210(1-0.0109)^t
Solve for t
t=12.77 =13 years
2010+13=2023

So the answer is c

Answer 2

The city population will first be below 48,000 in the year:

2022

Explanation:

It is given that:

In 2010, a city population was 55,210

in 2011 the city population will be

(100-1.09)×55210/100=98.91×55210/100

= 0.9891×55210

in 2012 the city population will be

0.9891×0.9891×55210

we have to find number of years t such that

`(0.9891)^(t)55210<48000\\\\(0.9891)^(t)<(48000)/(55210)\\\\(0.9891)^(t)<0.8694\\\\t=13`

i.e. the thirteen years from 2010 we will have city population less than 48000

i.e. in the year 2022