Question

every 5 years in march the population of a certain town is recorded in 1995 the town had a population of 4,500 people. from 1995-2000 the population increased by 15% from 2000-2005 the population decreased by 4% what was the towns population in 2005?

Answer 1

Year. Population
1995. 4,500
2000. 15% increase from 4,500
15% of 4500=0.15•4500=675
4500+675=
5,175
2005. 4% decrease from 5,175
4% of 5175=0.04•5175=207
5175-207=
4968

Answer 2

7379.

Explanation:

We have been given that every 5 years in march the population of a certain town is recorded in 1995 the town had a population of 4,500 people.

From 1995-2000 the population increased by 15%.

Let us find the population in 2000 using exponential growth formula.

`y=a*(1+r)^x`, where,

a = Initial amount or value,

r = Growth rate in decimal form.

Let us convert our given rate in decimal form.

`15\%=(15)/(100)=0.15`

`y=4500*(1+0.15)^(2000-1995)`

`y=4500*(1.15)^(5)`

`y=4500*2.0113571875`

`y=9051.10734375\approx 9051`

To find the population in year 2005 we will use exponential decrease function.

`y=a*(1-r)^x`, where,

a = Initial amount or value,

r = Decay rate in decimal form.

Let us convert our given rate in decimal form.

`4\%=(4)/(100)=0.04`

`y=9051*(1-0.04)^(2005-2000)`

`y=9051*(0.96)^(5)`

`y=9051*0.8153726976`

`y=7379.9382859\approx 7379`

Since we can not have 0.938 of a person, therefore, the population of town was 7379 in 2005.