Visitors enter a museum at a rate of people per hour
MATHEMATICS · Single correct · AP · Calculus AB · Applications of Integration · Applications of Integration
Problem
Visitors enter a museum at a rate of r(t)=150e−0.1t−20 people per hour, where t is the number of hours after the museum opens. The museum closes 10 hours after opening.
At what time in that 10-hour period, if any, does the cumulative number of visitors first reach 800?
(a) After approximately 8.8\,hours.
(b) The cumulative total does not reach 800 visitors within the first 10 hours.
(c) After approximately 6.2\,hours.
(d) After approximately 9.7\,hours.