A typical human heart pumps 70 mL of blood with each stroke (stroke volume). Assuming a heart rate of 60 beats/min (1 beat/s), a reasonable model for the outflow rate of the heart is V'(t) = 70(1 + sin 2πt), where V(t) is the amount of blood (in milliliters) pumped over the interval [0, t], V(0) = 0, and t is measured in seconds.

a. Graph the outflow rate function.

b. Verify that the amount of blood pumped over a one-second interval is 70 mL.

c. Find the function that gives the total blood pumped between t = 0 and a future time t > 0.

d. What is the cardiac output over a period of 1 min? (Use calculus; then check your answer with algebra.)