Question

Question ♀️ 4The Booneville History Museum had 25,000 visitors in 1980. The number of visitors has decreased by 2.5% each year since 1980. How many people visited in 1985?Round to the nearest whole number.

Answer 1

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;

`y_1=25000-(2.5\%*25000)=25000-((2.5)/(100)*25000)=24375`

So, as of 1982 (x = 2), the number of visitors would be;

`y_2=24375-((2.5)/(100)*24375)=23765.625`

So, as of 1983 (x = 3), the number of visitors would be;

`y_3=23765.625-((2.5)/(100)*23765.625)=23171.484375`

So, as of 1984 (x = 4), the number of visitors would be;

`y_4=23171.484375-((2.5)/(100)*23171.484375)=22592.197265625`

So, as of 1985 (x = 5), the number of visitors would be;

`y_5=22592.197265625-((2.5)/(100)*22592.197265625)=22027.39233398438`

To the nearest whole number, the number of people visited in 1985 is 22027

Alternatively,

If we use the Decay formula

`y=a(1-r)^x`

Here, a = 25,000, r = 2.5% and x = 5

`y=25000(1-(2.5)/(100))^5\approx22027`