Some work through this with me please?

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DEPRECIATION A machine that originally cost $15,600 has a value of $7500 at the end of 3 years. The same machine has a value of $2800 at the end of 8 years.

 

     a. Find the average rate of change in value (depreciation) of the machine between its purchase and the end of 3 years.

 

      b. Find the average rate of change in value of the machine between the end of 3 years and the end of 8 years.

 

     c. Interpret the sign of your answers.

Sep 3rd, 2015

Thank you for the opportunity to help you with your question!

a. The average rate of change will equal the change in cost divided by the number of years.  You want to determine how much less the machine costs each year.  You can use the basic 'rate' equation seen below, then plug in the given values:

time=3yrs            

cost2=$7500       cost of machine at end of 3 years

cost1=$15600     cost of machine originally

Rate=(cost2-cost1)/time

Rate=(7500-15600)/3

Rate = -$2700/yrs

b. Same concept for this question:

time=8-3=5yrs

cost1=$7500

cost2=$2800

Rate=(cost2-cost1)/time

Rate=(2800-7500)/5

Rate = -$940/yrs

c. Since the signs for questions a and b are negative, this means that the machine will cost less each year.  If looking at problem a, the answer means that for every one year, the machine costs $2700 less on average.


Please let me know if you need any clarification. I'm always happy to answer your questions.
Sep 3rd, 2015

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Sep 3rd, 2015
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Sep 3rd, 2015
Sep 26th, 2017
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