# Exercise 4.7.12. [S] [C][Section 4.2][Goal 4.2][(Goal 4.4] Firefighters' pay.On June 10, 2010 The Boston Globe reported that in the five years between 2006 and 2011Boston firefighters received raises of 2%, 2.5%, 3%, 3.5%, 2.5% and 1.5%.(a) Explain why the overall raise for this five year period is not just the sum of the six percentageincreases.What was the firefighters' overall raise for the five year period?(c) What was the firefighters' overall raise when you take inflation into account?[See the back of the book for a hint.]Coal 4 21Goal 4.4] A raise tied to the inflation rate.1 tn"10% over the rate of inflation":

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Step 1

Given that Boston fire fighters got a raise of 2%,2.5%,3%,3.5%,2.5%,1.5% from 2006 to 2011.

The over all raise for this five year period is not just the sum of all percetnages as the raise of 2%in 2006  is with respect to their pay in year 2005,  the percentage of raise 2.5% in 2007 is with respect to their pay in year 2006, the percentage of raise 3% in 2008 is with respect to their pay in year 2007 and so on. Here we can see that the percentage raise is compounding so we cannot just add percentages to get the overall percentage raise.

Step 2

let i1 i2 i3 i4 i5 i6  be  2%,2.5%,3%,3.5%,2.5%,1.5% respectively, the raise in pay of fire fighters from 2006 to 2011.

Let us assume the overall raise is given by i and the below a formula is mentioned to calculate the overall raise. After substituting the ...

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