Accumulation Functions, Definite Intervals, Applied Contexts Practice Test

A spherical balloon is being inflated. The rate of change of its radius is given by the function $$r'(t)$$, measured in centimeters per second. Which of the following represents the total increase in the balloon's radius from $$t=2$$ to $$t=6$$ seconds?

At 9 AM ($$t=0$$ hours), an online store has 500 orders to be processed. The rate at which orders are processed is given by $$P(t) = 20t + 50$$ orders per hour. Assuming no new orders arrive, how many orders are still waiting to be processed at 1 PM ($$t=4$$ hours)?