Question

A tank contains 24 gallons of water when all of a sudden the water begins draining at a constant rate of 2 gallons per hour. Let t represent the number of hours since the water began draining and let v represent the volume of water in the tank.
Required:
a. Write a formula that expresses v in terms of t.
b. As t increases from 3 to 6, v varies from _________ to _________

Answer 1

Answer:

a) $V(t) = 24 - 2t$

b) As t increases from 3 to 6, v varies from 18 gallons to 12 gallons.

Step-by-step explanation:

The volume of the tank in terms of the time can be described by the following equation:

$V(t) = V(0) - at$

In which V(0) is the initial volume and a is the hourly decrease rate.

a. Write a formula that expresses v in terms of t.

The tank initially contains 24 gallons of water, which means that $V(0) = 24$

Drains at a constant rate of 2 gallons per hour, so $a = 2$

Then

$V(t) = V(0) - at$

$V(t) = 24 - 2t$

b. As t increases from 3 to 6, v varies from _________ to _________

$V(t) = 24 - 2t$

$V(3) = 24 - 2*3 = 18$

$V(6) = 24 - 2*6 = 12$

So as t increases from 3 to 6, v varies from 18 gallons to 12 gallons.