Initially 100 milligrams of a radioactive substance was present. After 6 hours t
ID: 3120936 • Letter: I
Question
Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had decreased by 5%. If the rate of decay is proportional to the amount of the substance present at time t, determine the half-life of the radioactive substance. When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time r, that is, dS/dt = rS, where r is the annual rate of interest. (a) Find the amount of money accrued at the end of 6 years when $6000 is deposited in a savings account drawing 5 3/4% annual interest compounded continuously. (b) In how many years will the initial sum deposited have doubled? (c) Use a calculator to compare the amount obtained in part (a) with the amount S = 6000(1 + 1/4(0.0575))^6(4) that is accrued when interest is compounded quarterly.Explanation / Answer
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Dear Student Thank you for using Chegg !! Given Initial amount of radioactive substance = 100 mg Given that after 6 hours mass has decreased by 5% Mass after t time = 100 - 5%of 100 = 95 mg Also rate of decay is proportional to amount present at time t required : - Half Life of radioactive substance Since rate of decay is proportional to amount present at time t => P = P0 exp (-kt) P: Amount after time t 95 P0: Initial amount 100 k: Rate of Change k t: Time elapsed 6 95 100exp(-6k) 0.95 exp(-6k) Taking natural log both sides -0.051293294 = -6k k = 0.008549 Now for half life computation we know P = P0/2 Applying the same in formula 0.5 = exp(-0.008549t) Taking natural log both sides -0.693147181 = -0.008549t t = 81.07933 hours