5. Applications of Integrals

Accumulation Models — Quiz

Test your understanding of accumulation models with 5 practice questions.

Practice Questions

Question 1

If the rate of change of a population is given by $P'(t) = 4t + 2$, what is the total population after 3 years, starting from an initial population of 50?

Question 2

A company's revenue rate is modeled by $R'(t) = 100 - 5t$. What is the total revenue generated from time $t = 0$ to $t = 10$?

Question 3

If the rate of water flow into a tank is given by $f(t) = 3t^2 + 2$, how much water is in the tank after 4 minutes, assuming it starts empty?

Question 4

A car's speed is modeled by $v(t) = 50 + 3t$. What is the total distance traveled from $t = 0$ to $t = 5$ hours?

Question 5

If the rate of change of a company's profit is given by $P'(t) = 200 - 20t$, what is the total profit accumulated during the first 10 months?