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April 15th, 2014, 03:49 AM  #1 
Senior Member Joined: Sep 2013 From: Earth Posts: 827 Thanks: 36  Progression problem
Two companies, C and D, offer a different salary scale for the same post: Company C:Starting monthly pay = RM500.00 Thereafter, the monthly salary for a particular month is 10% more than the monthly salary for the preceding month Company D:Starting monthly pay = RM300.00 Thereafter, the monthly salary for a particular month is 15% more than the monthly salary for the preceding month (a)Azrin and Aidil start to work for company C and D respectively in the same month. After how many months will Aidil’s monthly salary be more than Azrin’s monthly salary? Use two methods. (b)Which salary scale is the better deal? Justify. 
April 16th, 2014, 08:02 AM  #2  
Math Team Joined: Dec 2006 From: Lexington, MA Posts: 3,267 Thanks: 407  Hello, jiasyuen! Quote:
These are geometric sequences. After $\displaystyle n$ months, Azrin's monthly salary is: $\displaystyle \,500(1.10^n)$ dollars. After $\displaystyle n$ months, Aidil's monthly salary is: $\displaystyle \,300(1.15^n)$ dollars. When is Aidil's salary greater than Azrin's? $\displaystyle \quad 300(1.15^n) \;>\; 500(1.10^n) \quad\Rightarrow\quad \frac{1.15^n}{1.10^n} \;>\;\frac{500}{300}$ $\displaystyle \quad \left(\frac{1.15}{1.10}\right)^n \;>\;\frac{5}{3} \quad\Rightarrow\quad \left(\frac{23}{22}\right)^n \;>\;\frac{5}{3} $ Take logs: $\displaystyle \:\ln\left(\frac{23}{22}\right)^n \;>\; \ln\left(\frac{5}{3}\right) \quad\Rightarrow\quad n\ln\left(\frac{23}{22}\right) \;>\;\ln\left(\frac{5}{3}\right)$ $\displaystyle \quad n \;>\;\frac{\ln\left(\frac{5}{3}\right)}{\ln\left( \frac{23}{22}\right)} \;=\;11.491684...$ Aidil's salary will be greater in 12 months. Quote:
If they plan to work for less than one year, $\displaystyle \quad$ Company C has the better deal. Otherwise, Company D's deal is better.  

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(a) azrin and aidil start to work for company c and d respectively in the same month. after how many months will aidil’s monthly salary be more than azrin’s monthly salary? use two methods.,salary scheme with geometric sequence
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