2014-01-17

An energy company uses exponential power.


Question 

In Rabbit city, Mr Fox generates electricity energy. One day, Mr Fox realized there is no one else generates the energy. So he decided  raise the price every year for 30 years since that year he retire. He met his uncle, who is working for the city hall. Mr Fox said his uncle, ``I would like to raise the price 10 Euro for currently 100 Euro paying rabbit.'' His uncle answered, ``It seems you don't know about economy. You should say, I will raise 10 % every year.'' Which statement of following is correct? Mark all apply.
  1. It's same raise when you start 100 Euro and 10 Euro every year and when you start 100 Euro and 10% raise every year. Since 10% of 100 Euro is 10 Euro. Therefore, 30 years later, how much raise the price is 10 * 30 = 300, and plus original price 100 = 400. It becomes 400 Euro after 30 years.
  2. Mr. Fox's uncle is correct. 30 years later, 10% every year raise is twice as much as 10 Euro each year's raise. The raised cost is around 600 Euro and the cost becomes 700 Euro.
  3. Mr. Fox's uncle is correct. 30 years later, 10% every year raise is five times more than 10 Euro each year raise.

Answer

10% every year is much higher raise than 10 Euro each year raise.

  1. First year raise: 100 * 0.1 = 10, + principle price 100 Euro = 110 Euro.
  2. Second year raise: The price is now 110, so 110 * 0.1 = 11, + current price 110 Euro = 121 Euro.
  3. Third year raise: The price is now 121, so 121 * 0.1 = 12.1, + current price 121 Euro = 133.1 Euro.
  4. n-th year price can be calculated by $100*(1.1)^n$. 30 years later, the price is $100*(1.1)^{30}$ = 1744.9 Euro.

Do you understand why Mr Fox's uncle suggested 10% raise instead of 10 Euro every year?  Some people use this trick as ``Every year, the same raise, 10%.''  It sounds like every year the same absolute price raise, but, actually every year you pay more and more. If you learn math, please don't be cheated.

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