Question

In the first week of its release, the latest blockbuster movie sold $16.3 million dollars in tickets. the movie's producers use the formula pt = poe-0.4t to predict the number of ticket sales t weeks after a movie's release. po is the first week's ticket sales. what are the predicted ticket sales to the nearest $0.1 million for the sixth week of this movie's release? (note: t = 0 for the first week.)

Answer 1

First you must make use of the exponential equation that gives you the problem, there you will define that for t = 0 you are in the first week. Therefore, there you have $ 16.3 million. For the sixth week you are at t = 5 and there you must evaluate the exponential equation for that time value (t = 5). The result will be the sale of tickets for the sixth week. The procedure is attached.

Answer 2

$2.2 million tickets will be sold in 6th week.

Explanation:

The given formula
`p(t) = p(0)e^(-0.4t)`

p(t) = Tickets sold after time t

p(0) = Tickets sold in first week

t = duration or time

For t = 0 [for 1st week]

p(0) = $16.3 million

For t = 6 weeks

Since for 1st week, t = (1 - 1) = 0

Therefore, for 6th week t = ( 6 - 1) = 5

By placing the values in the formula,

p(5) =
`16.3* e^(-0.4* 5)`

=
`16.3* e^(-2)`

= 16.3×0.1353

= $2.2 millions

Therefore, $2.2 millions of tickets will be sold in the sixth week.