Science:Math Exam Resources/Courses/MATH104/December 2011/Question 01 (h)
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Question 01 (h) 

You bought a rare stamp collection for 10 million dollars. The auctioneer who sold it to you estimated its value would increase at 12% per year, compounded continuously. If you want to wait until the collection has tripled in value before you sell, how many years will you be waiting? 
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 

Which formula would you use to calculate continuously compounded interest? Once you have that formula, which variable are you solving for? 
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 

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Please rate my easiness! It's quick and helps everyone guide their studies. Let the value of the stamp collection at time t be v(t), and the time at which the collection was purchased be time t = 0. Then million dollars, and If we wait until the collection has tripled in value, then we would be waiting until million dollars. So, we solve the following equation for t: Therefore, we'll be waiting years. Note: This is a little more than 9 years. Also, using the rules of logarithms, we could also express the solution as Whether this simplification would be necessary is up to your instructor. 