Answer:
7379.
Step-by-step 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.
[tex]y=a*(1+r)^x[/tex], where,
a = Initial amount or value,
r = Growth rate in decimal form.
Let us convert our given rate in decimal form.
[tex]15\%=\frac{15}{100}=0.15[/tex]
[tex]y=4500*(1+0.15)^{2000-1995}[/tex]
[tex]y=4500*(1.15)^{5}[/tex]
[tex]y=4500*2.0113571875[/tex]
[tex]y=9051.10734375\approx 9051[/tex]
To find the population in year 2005 we will use exponential decrease function.
[tex]y=a*(1-r)^x[/tex], where,
a = Initial amount or value,
r = Decay rate in decimal form.
Let us convert our given rate in decimal form.
[tex]4\%=\frac{4}{100}=0.04[/tex]
[tex]y=9051*(1-0.04)^{2005-2000}[/tex]
[tex]y=9051*(0.96)^{5}[/tex]
[tex]y=9051*0.8153726976[/tex]
[tex]y=7379.9382859\approx 7379[/tex]
Since we can not have 0.938 of a person, therefore, the population of town was 7379 in 2005.
