Ice forms on a refrigerator ice-box at the rate of (4−0.6t) g per minute after t minutes. If initially there are 2 g of ice in the box, find the mass of ice in the box after 5 minutes.
Worked solution (try it first)
The rate is the derivative of the mass, so integrate it to find the ice formed from t=0 to t=5.
∫(4−0.6t)dt=4t−0.3t2.
At t=5 this is 20−7.5=12.5, and at t=0 it is 0.
So 12.5 g of ice forms.
Add the 2 g already there: 2+12.5=14.5 g, option C.