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March 27th, 2014, 02:06 AM  #1 
Newbie Joined: Mar 2014 Posts: 12 Thanks: 0  Given the data  Answer the following / please explain http://www.essentialprep.com/quant/top ... _doc2.html Given the data above, answer the following: 1) By what constant rate of change were sales increasing, year over year? By what constant amount were ln(sales) increasing, year over year? Answer is +7%,+0.07 Note: it's using the natural logarithm, where e=2.718281828 2) With the data above calculate ln(sales) and sales (in cases) predicted this year [color=#0040FF]12.78 353,938[/color] Predicted next year [color=#0040FF]12.85 378,714[/color] Predicted two years from now [color=#0040FF]12.92 405,224[/color] Please explain the above solutions in blue  I'm not able to understand. 3) Given this growth rate, in how many years from now will Pine Cola's annual sales exceed half a million cases? So a total of 3 questions. 
March 27th, 2014, 04:05 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 20,966 Thanks: 2216 
The values of ln(sales), rounded to two decimal places, are 12.43, 12.50, 12.57, 12.64, 12.71, [color=blue]12.78, 12.85, 12.92, 12.99, 13.06, 13.13, etc.[/color] (I successively added 0.07 to get the blue figures.) The blue figures for sales (in cases) were obtained similarly by multiplying by 1.07 and rounding to the nearest integer. As the approximately constant rate of change was about 7.2508%, using 7% gives predicted values that rapidly become out of step with the predicted values of ln(sales). Do you wish to answer the third question by using the predicted values for ln(sales) or the predicted values for sales (in cases)? 
March 28th, 2014, 10:35 PM  #3 
Newbie Joined: Mar 2014 Posts: 12 Thanks: 0  The question is asking for number of years and the answer is 7. I think you will arrive at the same using either methods, but I think in cases would be the preferred way to solve the problem.

March 29th, 2014, 05:45 PM  #4  
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  Quote:
330783(1.07)^n = 500000 1.07^n = 500000/330783 n = LOG(500000/330783) / LOG(1.07) n = 6.106... So early in 7th year...  

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