A brilliant chemist, Sir Nigel Worthington Price has re- cently discovered Nigelite, a radioactive isotope which...

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A brilliant chemist, Sir Nigel Worthington Price has re- cently discovered Nigelite, a radioactive isotope which loses 20.63% of the quantity present, every week. (a) If Q(t) is the amount of Nigelite present in week t, and Qo is the initial quantity present, find a formula for Q(t), without using the number e. (b) At what continuous decay rate is the amount of Nigelite decreasing? (c) Sir Nigel defined a constant he found particularly useful in some peculiar research he was doing. He called it "Nigel's Life". Nigel's Life is defined to be the amount of time needed for any amount of Nigelite to decay to 1/e of its original amount. With- out doing any calculations, decide if Nigel's Life is larger or smaller than the half-life of Nigelite. Give a reason for your answer. (d) Calculate Nigel's Life. Give an exact answer as well as a decimal approximation containing at least one decimal place. A brilliant chemist, Sir Nigel Worthington Price has re- cently discovered Nigelite, a radioactive isotope which loses 20.63% of the quantity present, every week. (a) If Q(t) is the amount of Nigelite present in week t, and Qo is the initial quantity present, find a formula for Q(t), without using the number e. (b) At what continuous decay rate is the amount of Nigelite decreasing? (c) Sir Nigel defined a constant he found particularly useful in some peculiar research he was doing. He called it "Nigel's Life". Nigel's Life is defined to be the amount of time needed for any amount of Nigelite to decay to 1/e of its original amount. With- out doing any calculations, decide if Nigel's Life is larger or smaller than the half-life of Nigelite. Give a reason for your answer. (d) Calculate Nigel's Life. Give an exact answer as well as a decimal approximation containing at least one decimal place.