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1)A cup of coffee at...

1)A cup of coffee at 195 degrees is poured into a mug and left in a room at 72 degrees. After 1 minutes, the coffee is 144 degrees. Assume that the differential equation describing Newton's Law of Cooling is (in this case) dT/dt=k(T−72). What is the temperature of the coffee after 11 minutes? After how many minutes will the coffee be 100 degrees?

2)The half-life of Radium-226 is 1590 years. If a sample contains 200 mg, how many mg will remain after 1000 years?

**Hint:** Recall P=P0ekt where P0 is the initial amount of such a substance, P is the amount at a given time t andk is the exponential rate of decay. What would it mean if P=.5P0?

3)Scintillatium has a halflife of 11 minutes. If a sample has 800 grams, find a formula for its mass after t minutes.

How much is left after 60 minutes?

When will there be 50 grams left?

4)Oil is pumped continuously from a well at a rate proportional to the amount of oil left in the well. Initially there were 1 million barrels of oil in the well; six years later 500,000 barrels remain.

**(a)** At what rate was the amount of oil in the well decreasing when there were 600,000 barrels remaining?

rate = barrels/year

**(b)** When will there be 50,000 barrels remaining?

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