Show all work in detail. Ans: a) r=ln2 b)R(t)=0.5e^(-t ln2) c)0.723rad

(a) Recall from last term that radioactive material decays according to a negative exponen- tial: m(t) = mo . earl, where m(t) is the mass of the radioactive material at time t, mo = m(0) is the initial mass at time { = 0, and r is the rate of decay. The half-life is the time it takes for the material to decay to one half its initial mass. Suppose that & is measured in months. Determine the rate of decay r if the half-life is 1 month. (b) Assume that at any time, the amount of radiation is proportional to the mass of the radioactive material. If initially the radiation level is 0.5 rads per month, how could we describe the radiation level as a function of time? (c) Assume now that there is radioactive material in your backyard of the type considered in (a) above, i.e. that it has a half-life of one month. Calculate the cumulative exposure in rads that would occur if you lived in your house for 10 years