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Radioactive cobalt 60 has a half-life of \(5.3\) years. Find its decay constant.

Currently, 1800 people ride a certain commuter train each day and pay $$\$ 4$$ for a ticket. The number of people \(q\) willing to ride the train at price \(p\) is \(q=600(5-\sqrt{p})\). The railroad would like to increase its revenue. (a) Is demand elastic or inelastic at \(p=4 ?\) (b) Should the price of a ticket be raised or lowered?

Ten thousand dollars is deposited in a money market fund paying \(8 \%\) interest compounded continuously. How much interest will be earned during the second year of the investment?

Differential Equation and Decay The amount in grams of a certain radioactive material present after \(t\) years is given by the function \(P(t)\). Match each of the following answers with its corresponding question. Answers a. Solve \(P(t)=.5 P(0)\) for \(t\). b. Solve \(P(t)=.5\) for \(t\). c. \(P(.5)\) d. \(P^{\prime}(.5)\) e. \(P(0)\) f. Solve \(P^{\prime}(t)=-.5\) for \(t\). g. \(y^{\prime}=k y\) h. \(P_{0} e^{k t}, k<0\) Questions A. Give a differential equation satisfied by \(P(t)\). B. How fast will the radioactive material be disintegrating in \(\frac{1}{2}\) year? C. Give the general form of the function \(P(t)\). D. Find the half-life of the radioactive material. E. How many grams of the material will remain after \(\frac{1}{2}\) year? F. When will the radioactive material be disintegrating at the rate of \(\frac{1}{2}\) gram per year? G. When will there be \(\frac{1}{2}\) gram remaining? \(\mathbf{H}\). How much radioactive material was present initially?