Question

a new play premieres on saturday, october 1, and 420 people attend. attendance then decreases by 30% each day. find the attendance on tuesday , october 4

Answer 1

The attendance on tuesday, october 4, is of 144 people.

Explanation:

The attendance after t days is given by the following equation:

`A(t) = A(0)(1-r)^(t)`

In which A(0) is the attendance on the first day and r is the daily decrease rate.

Premieres on saturday, october 1, and 420 people attend.

This means that
`A(0) = 420`

Attendance then decreases by 30% each day.

This means that
`r = 0.3`

So

`A(t) = A(0)(1-r)^(t)`

`A(t) = 420(1-0.3)^(t)`

`A(t) = 420(0.7)^(t)`

Find the attendance on tuesday , october 4

This is 4-1 = 3 days after saturday. So this is A(3).

`A(3) = 420(0.7)^(3) = 144`

The attendance on tuesday, october 4, is of 144 people.