Science:Math Exam Resources/Courses/MATH100/December 2012/Question 05 (b)
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Question 05 (b) 

FullSolution Problems. In questions 511, justify your answers and show all your work. If a box is provided, write your final answer there. Unless otherwise indicated, simplification of numerical answers is required in these questions. 5. A sample of the radioactive substance Rhodium101 decayed to 12.5% of its original amount after 10 years. (b) What is the halflife of Rhodium101? Remember to simplify your answer completely. 
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 hints below. Read the first one and consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it! If after a while you are still stuck, go for the next hint. 
Hint 1 

(For Solution 1) Using the values of C and k you found in part (a), try to modify the formula so that it is written in the form (where K will be a number different than the original k from part (a)). 
Hint 2 

(For Solution 2) Using the values of C and k you found in part (a), use the formula to solve for t when y(t) = 50. 
Checking a solution serves two purposes: helping you if, after having used all the hints, 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. From part a, we know that
Writing as a power of 1/2, we have
In order for the rightmost expression to give us 50, the exponent needs to equal 1. Thus, the value of t that gives is 
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. From part a, we have
Because y(t) represents the percentage of Rhodium101 remaining at time t, to find halflife (which is when there is 50% remaining), we set and solve for t. completing the question. 