Question

A theater's profit is modeled by P(t)=−t2+100t−1600
. Based on the graph, what is one ticket price that yields a profit of $500?

Graph showing the relationship between ticket price and profit.
(1 point)
Responses

$40
$40

$20
$20

$50
$50

$30

Answer 1

Set −t^2 + 100t − 1600 = 500. Solving gives t^2 − 100t + 2100 = 0 with roots t = (100 ± 40)/2 = 70 or 30.

One ticket price is $30.