00:01
Hi, here we have the following problem.
00:04
An electricity company charges its customers a base rate of $10 a month, plus $6 per kilowatts per hour for the rest, 1 ,200 kilowatts, and 7 cents per kilowat for all users are over 1 ,200 kilowatts.
00:25
And we want to express the monthly cost as a function of the amount of the amount x of electricity use and then graph the function the cost function which we will denote by e for x between 0 and 2 000 so this is so x here is the the units of electricity use and what we have if x is between 0 and 1200 we get the basic rate 10 so if x for example is equal to 0 we only get 10 and then for anything above zero and up to 1200 it is charged 0 .06 dollars per unit i have made them because 10 is in dollars i put the six cents i express it as dollars so this actually gives us the cost in in dollars okay so this is what happens if x is between if the consumption is anything between zero and 1200.
01:36
If it is zero, you only pay 10.
01:38
Then if you consume more or anything above zero and below or equal to 1200, you pay so much.
01:48
And then what happens if x exceeds 1 ,200? well, the first 1 ,200 units, so if x exceeds 1 ,200, you still have to pay the $10 ,000, basic rate, the first 1200 units are charged by $0 .06 per unit.
02:13
And then all the units above 1200, they will be charged by $0 .07.
02:22
And the unit, the number of units above $1 ,200 is what? if your x is above 1200, the units above 1200, the unit above 1200 is going to be the number of units going to be the difference between x and 1200 and so the cost function is actually a function that it is graph piece wise it is defined piecewise and now let's try to graph it for x between 0 and 2 000 so what we are going to do here i will actually try to find few values of the function we have that e of 0 is equal to 10 from here then e of 1200 i'm going to use this part of the definition to find e of 1200 is equal this is an easy calculation is equal to 82 and then i'm going to have e of let's say e of, yes, i want 2000...