AP CALC AB: Interpretations & Applications of the Derivative & Definite Integral

Question

How would you solve for a) & b) with a calculator?

I have a TI-89 Titanium.

At time t=0, a tank contains 38 gallons of water. Beginning at t=0, water flows into the tank at a rate of

E(t) = 12tsin(π/4t) gallons per minute, and water leaks out of the tank at a rate of L(t) = 6t²/ (t+2) gallons per minute.

a) How many gallons of water are in the tank at time t = 2 minutes?

b) What is the rate of change in the volume of water in the tank at t = 2 minutes? (Include appropriate units)

Answer 1

Net rate of change (in gallons/min) = V^'(t) = E(t) - L(t)

a) V(2) = 38 + ∫₀² (E(t) - L(t))dt

b) V^'(2) = E(2) - L(2) (in gallons/min)