Question

If a tank holds 5000 gallons of water, which drains from the bottom of the tank in 40 minutes, then Torricelli's Law gives the volume V of water remaining in the tank after t minutes as V=5000(1−t40)20≤t≤40. Find the rate at which water is draining from the tank after the following amount of time. (Remember that the rate must be negative because the amount of water in the tank is decreasing.)

Answer 1

V'(t) =
`-250(1 - (1)/(40)t)`

If we know the time, we can plug in the value for "t" in the above derivative and find how much water drained for the given point of t.

Explanation:

Given:

V =
`5000(1 - (1)/(40)t )^2` , where 0≤t≤40.

Here we have to find the derivative with respect to "t"

We have to use the chain rule to find the derivative.

V'(t) =
`2(5000)(1 - (1)/(40) t)d/dt (1 - (1)/(40)t )`

V'(t) =
`2(5000)(1 - (1)/(40) t)(-(1)/(40) )`

When we simplify the above, we get

V'(t) =
`-250(1 - (1)/(40)t)`

If we know the time, we can plug in the value for "t" and find how much water drained for the given point of t.