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A radioactive substance decays in such a way that the amount of mass remaining after tt days is given by the function m(t)=12e−0.017tm(t) = 12e^{-0.017t} where m(t)m(t) is measured in kilograms. (a) Find the mass at time t=0t = 0. 1212 Correct: Your answer is correct. kg (b) How much of the mass remains after 5050 days? (Round your answer to one decimal place.) 1.71.7 Incorrect: Your answer is incorrect. kg

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Q. A radioactive substance decays in such a way that the amount of mass remaining after tt days is given by the function m(t)=12e−0.017tm(t) = 12e^{-0.017t} where m(t)m(t) is measured in kilograms. (a) Find the mass at time t=0t = 0. 1212 Correct: Your answer is correct. kg (b) How much of the mass remains after 5050 days? (Round your answer to one decimal place.) 1.71.7 Incorrect: Your answer is incorrect. kg
  1. Substitute t=0t = 0: To find the mass at time t=0t = 0, we need to substitute t=0t = 0 into the decay function m(t)=12e−0.017tm(t) = 12e^{-0.017t}.\newlineCalculation: m(0)=12e−0.017×0=12e0=12×1=12m(0) = 12e^{-0.017 \times 0} = 12e^0 = 12 \times 1 = 12
  2. Find mass at t=0t = 0: Now, to find the mass remaining after 5050 days, we substitute t=50t = 50 into the decay function.\newlineCalculation: m(50)=12e(−0.017×50)m(50) = 12e^{(-0.017 \times 50)}
  3. Substitute t=50t = 50: We need to calculate the exponent first: −0.017×50=−0.85-0.017 \times 50 = -0.85
  4. Find mass at t=50t = 50: Now we calculate e(−0.85)e^{(-0.85)} using a calculator or a computational tool.\newlineCalculation: e(−0.85)≈0.4265e^{(-0.85)} \approx 0.4265 (rounded to four decimal places for intermediate calculation)
  5. Calculate exponent: Next, we multiply the result by 1212 to find the mass remaining after 5050 days.\newlineCalculation: 12×0.4265≈5.11812 \times 0.4265 \approx 5.118 (rounded to three decimal places)
  6. Calculate e−0.85e^{-0.85}: Finally, we round the answer to one decimal place as the problem asks.\newlineCalculation: 5.1185.118 rounded to one decimal place is 5.15.1

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