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QCE Stuff => QCE Mathematics Subjects => QCE Subjects + Help => QCE Mathematical Methods => Topic started by: d_gridley on March 27, 2021, 05:51:53 pm
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Is someone able to help work through this question for me please?
Thanks.
The mass, m mg, of a radioactive substance remaining in a sample t hours after observations began is
given by the rule m.t/ = ae−kt. Initially, 30 mg of the substance is present. After 2 hours the scientist
observes that 20% had disintegrated.
a. State the value of a.
b. Determine the mass of the substance after 2 hours.
c. Calculate the value of k, correct to 4 decimal places.
d. Determine the amount of the substance remaining after a further 3 hours. Give your answers correct
to 2 decimal places.
e. Determine when the rate of decay of the substance is 1 mg/hour. Give your answer correct to
1 decimal place.
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Hey d_gridley,
a) to find the value of a, look at the values that we know. We know that initially t = 0, and at that point in time m(0) = 30. You can substitute those values in to calculate a (generally, the value for a will be the initial amount, however you can use this process to prove that)
b) after two hours, 20% has disintegrated. Therefore, what's left over will be 80% of the initial amount
c) after completing parts a and b, you can use t = 2, m(2) = 80% of initial, and the calculated value for a to solve for k.
d) once you have calculated k you can sub that into the equation and solve for t = 3.
e) derive the equation and set it equal to 1 to determine the value for t that has a rate of decay of 1mg/hr
Hope this helps - give us a shout if you are still having some troubles,
Katelyn