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1. (5) The half-life of radium is 1700 years. Assume that the decay rate is proportional...

1. (5) The half-life of radium is 1700 years. Assume that the decay rate is proportional to the amount present. The initial amount is 5 grams. Let A(t) = amount remaining at time t:
(a) Set up the DE. Write your answer in the box.
(b) Solve the DE. Show your work. Simplify your answer. Do not solve for c and k yet. Write your answer in the box.
A(t) =
(c) Use the conditions to solve for the unknown constants c and k: Show your work. Simplify your answer. Write your answer in the box.
A(t) =
(d) When will 3 grams be left? Show your work. Write your answer in the box.
t =
2. (5) A large tank is partially lled with 100 gallons of uid in which 10 pounds of salt is dissovled. Brine containing 1 2 pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution leaves the tank at the rate of 4 gal/min. Let A(t) = amount of salt in the tank at time t: Set up the DE using the following steps. Show your work. Simplify your answers. Write your nal answers in the boxes.
(a) rin =
(b) rout =
(c) V (t) =
(d) c(t) =
(e) Rin =
(f) Rout =
(g) Write the DE.
dA dt =

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