Science:Math Exam Resources/Courses/MATH100/December 2016/Question 03 (b)
• Q1 (a) • Q1 (b) • Q1 (c) • Q2 (a) • Q2 (c) • Q2 (d) • Q3 (a) • Q3 (b) • Q3 (c) • Q4 (a) • Q4 (b) • Q4 (c) • Q5 (a) • Q5 (b) • Q5 (c) • Q6 (a) • Q6 (b) • Q7 (a) • Q7 (b) • Q8 • Q9 (a) (i) • Q9 (a) (ii) • Q9 (a) (iii) • Q9 (b) (i) • Q9 (b) (ii) • Q9 (b) (iii) • Q9 (c) (i) • Q9 (c) (ii) • Q9 (c) (iii) • Q10 (a) • Q10 (b) • Q11 (a) • Q11 (b) • Q12 • Q13 (a) • Q13 (b) • Q14 (a) • Q14 (b) • Q2 (b) •
Question 03 (b) 

A scientist isolates 32 grams of a radioactive substance in the lab at 1PM. At 5PM it weighs 4 grams. What is the halflife of the substance? 
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you? 
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! 
Hint 

The amount of radioactive substance remaining decays exponentially. 
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.

Solution 1 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. In 4 hours the sample decays by a factor of . This means the the sample decays by a factor of in hours. In other words, the halflife is minutes. 
Solution 2 

Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies. By the exponential decay formula we have When we have and at we have Dividing the first equation by the second gives
Now since halflife is given by , we have and so
