
Math General Math Forum  For general math related discussion and news 
 LinkBack  Thread Tools  Display Modes 
January 16th, 2017, 05:01 AM  #1 
Newbie Joined: Jan 2017 From: iraq Posts: 1 Thanks: 0  Average of percentage
Dear friends, I know this question is very simple but I will ask it hope not to misunderstand, recently I involved in a test which one of the questions like below: a company revenue growth percentage were 30%, 10% and 90% within 3 years continuously what is the percentage of average yearly growth. I know average is adding all numbers and divide by the number of years, but in the test there were not answer options like that. the answer options were 25, 20, 35, 40. I don't remember exactly. 
January 16th, 2017, 05:47 AM  #2 
Math Team Joined: Jul 2011 From: Texas Posts: 2,816 Thanks: 1460 
I'd say the correct choice is about 40%. Coming to a solution is not as easy as one would think ... Let $R$ represent the initial revenue ... Year 1 growth of 30% yields a new revenue of $1.3 \cdot R$ Year 2 growth of 10% yields a new revenue of $1.1 \cdot (1.3 \cdot R) = 1.43 \cdot R$ Year 3 growth of 90% (wow!) yields a new revenue of $1.9 \cdot (1.43 \cdot R) = 2.717 \cdot R$ So, for the 3 year period, $R$ increased by a factor of $2.717$ Let $a$ be the average yearly growth factor ... $a^3 = 2.717 \implies a \approx 1.3954 \implies$ average yearly growth percentage is about 39.54%. To check, say $R=\$100$ growth rate of revenue about 39.54% per year ... $\$100 \cdot 1.3954^3 = \$271.70$ 

Tags 
average, percentage 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Weighted Average Percentage  help  neil1975  Elementary Math  2  February 25th, 2016 07:27 AM 
Why does this percentage not average to 0%?  Apple30  Elementary Math  4  January 22nd, 2015 06:04 PM 
Average speed  Mr Davis 97  Physics  1  April 27th, 2014 12:58 AM 
Average  SidT  Elementary Math  5  August 17th, 2008 03:16 AM 
Average percentage  uneven credits  ritchie888  Algebra  1  June 18th, 2008 03:31 PM 