linear equations

Question

A quarterly electricity bill shows the following charges:
 For the first 50 kWh (kilowatt hours): 9.10c per kWh
 For the next 150 kWh: 5.80c per kWh
 Thereafter: 3.56c per kWh

a Write down a formula relating cost, $C, to n, the number of kWh of electricity used:
i for the first 50 kWh
ii for the next 150 kWh
iii for more than 200 kWh.
b Draw a graph of C against n. Use

Answer 1

What you are trying to graph is a "piecewise" defined
function; that is, a function that is defined by different
rules over different intervals over the domain. For
this problem, the domain is "n", the number of kWh,
or the x-axis values. The range is "$C" (in dollars), the 

total cost, or y-axis values.

a-i)  For the interval 0 < n ≤ 50:
$C=0.0910n.........................Eq1

a-ii)  For the interval 50 < n ≤ 200:
$C=0.0910(50)+0.0580(n-50)
     =4.55+0.0580(n-50)
     =4.55+0.0580n-2.90
     =0.0580n+1.65...............Eq2

a-iii)  For the interval n > 200:
$C=(0.0910(50)+0.0580(150))+0.0356(n-200)
     =(4.55+8.70)+0.0356(n-200)
     =13.25+0.0356(n-200)
     =13.25+0.0356n-7.12
     =0.0356n+6.13...............Eq3

 

Each of the above equations are in "slope-intercept" form 

with the slope value varying (and, hence, the y-intercepts)

from equation to equation.  They are ONLY valid over the

defined intervals.

 

b)  The graph of the above "Piecewise Function" can be

viewed at the following URL: 

 

https://www.wyzant.com/resources/files/416054/graph_of_piecewise_function

 

Set up a table for each equation and calculate "$C" values

for different "n" values.  Plot those points over the defined

intervals for each equation.