Solution
Given that:
Booneville History Museum had 25,000 visitors in 1980
This means that as of 1980 (x = 0) the number of visitors is 25,000 in number.
The question further states that; The number of visitors has decreased by 2.5% each year since 1980
This means that as of 1981 (x = 1) the number of visitors decreased by 2.5%.
Mathematically, the number of visitors would be;
[tex]y_1=25000-(2.5\%\times25000)=25000-(\frac{2.5}{100}\times25000)=24375[/tex]So, as of 1982 (x = 2), the number of visitors would be;
[tex]y_2=24375-(\frac{2.5}{100}\times24375)=23765.625[/tex]So, as of 1983 (x = 3), the number of visitors would be;
[tex]y_3=23765.625-(\frac{2.5}{100}\times23765.625)=23171.484375[/tex]So, as of 1984 (x = 4), the number of visitors would be;
[tex]y_4=23171.484375-(\frac{2.5}{100}\times23171.484375)=22592.197265625[/tex]So, as of 1985 (x = 5), the number of visitors would be;
[tex]y_5=22592.197265625-(\frac{2.5}{100}\times22592.197265625)=22027.39233398438[/tex]To the nearest whole number, the number of people visited in 1985 is 22027
Alternatively,
If we use the Decay formula
[tex]y=a(1-r)^x[/tex]Here, a = 25,000, r = 2.5% and x = 5
[tex]y=25000(1-\frac{2.5}{100})^5\approx22027[/tex]
