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1. Determine the values of r, if any, such that y = erx is a solution of the differential equations given below.

a. y" + 6y' + 9y = 0

b. y" - 5y' + 6y = 0

c. y"' - 3y' + 2y = 0

2. A tank with a 1"0-gal capacity initially contains 5" gal of water that is polluted with 50 lb of particulate matter. At time t = 0, pure water is added at a rate of 20 gal/min and the mixed solution is drained off at a rate of 10 gal/min.

How much particulate matter is in the tank when it reaches the point of overflowing?

4. Polonium-210 is a radioactive element with a half-life of 140 days. Assume that 20 milligrams of the element are placed in a lead container and that y(t) is the number of milligrams present t days later.

a. Find a formula for y(t).

b. How many milligrams will be present after 12 weeks?

c. How long will it take for 75% of the original sample to decay?

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