Water is pumped into a cylindrical tank, and then drained out. Suppose the volume of water in the tank in cubic meters after $t$ hours is given by the equation $$V(t)=-0.064t^3+0.256t^2-0.862 t+7.$$ Using an online tool like Desmos, sketch a graph of $V(t)$ on the interval $[0,8]$.

a) Find and interpret the maximum value of $V(t)$ on this interval.
Maximum value: ? cubic feet feet hours
We can interpret this as:

A. the most water in the tank at any time in the given time interval is the initial amount.
B. the amount of time it takes for all of the water to drain from the tank is 7 hours.
C. the height of the tank in feet is 7 feet.
D. the fastest the water is draining at any time in the given time interval is 7 feet per second.

b) Interpret both the vertical and horizontal intercepts of $V(t)$ in the context of the problem.

The vertical intercept:

A. is the amount of water left in the tank after 7 hours.
B. is the amount of time it takes for all of the water to drain from the tank.
C. is the initial volume of water in the tank.
D. is the fastest speed at which the water is draining from the tank.

The horizontal intercept:

A. is the initial volume of water in the tank.
B. is the amount of water left in the tank after 7 hours.
C. is the fastest speed at which the water is draining from the tank.
D. is the duration of time in hours it takes for all of the water to drain from the tank.

Hint: