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

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;

$y_1=25000-(2.5\%\times25000)=25000-(\frac{2.5}{100}\times25000)=24375$

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

$y_2=24375-(\frac{2.5}{100}\times24375)=23765.625$

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

$y_3=23765.625-(\frac{2.5}{100}\times23765.625)=23171.484375$

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

$y_4=23171.484375-(\frac{2.5}{100}\times23171.484375)=22592.197265625$

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

$y_5=22592.197265625-(\frac{2.5}{100}\times22592.197265625)=22027.39233398438$

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

$y=25000(1-\frac{2.5}{100})^5\approx22027$