A school can get its electricity from one of two companies, Buzz or Lecky - Junior Cycle Mathematics - Question 8 - 2017
Question 8
A school can get its electricity from one of two companies, Buzz or Lecky. The graphs below show the cost of the electricity per month from each company, if the scho... show full transcript
Worked Solution & Example Answer:A school can get its electricity from one of two companies, Buzz or Lecky - Junior Cycle Mathematics - Question 8 - 2017
Step 1
State which company charges no fixed fee.
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Answer
The company that charges no fixed fee is Lecky.
Reason: Lecky cuts the y-axis at (0, 0), indicating that there is no initial cost before charging for the units used.
Step 2
Write down the domain and the range of the function b(x).
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Domain:0≤x≤1000 Range:50≤b(x)≤325
Step 3
Use the graphs to estimate the set of values of x ∈ ℝ for which b(x) < l(x).
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The set of values for which b(x)<l(x) is approximately in the interval (100, 800).
Step 4
Explain what your answer to part (c)(i) means about the cost of electricity from Buzz and Lecky.
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When the number of units used is between 100 and 800, Buzz is cheaper than Lecky for the electricity cost. This means the school would save money by choosing Buzz for that range of consumption.
Step 5
Find the slope of the graph of b(x).
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The slope of the graph of b(x) can be calculated as follows:
Using two points on the line, for example, (0, 50) and (1000, 325):
Explain what your answer to part (d)(i) means about the cost of electricity from Buzz.
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The slope of 0.275 indicates that the cost of electricity rises by €0.275 for every one unit increase in usage. This means that for each additional unit of electricity consumed, the monthly cost increases steadily by this rate.
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