Can I get some help solving this massive problem please? Thanks!
1 Answer
See below:
Explanation:
The gas company, regardless of how much gas you use in a single month, charges a monthly service charge of $8.80. No matter what, we have to pay that.
The gas company then has a 2-tier system of charging for gas - if you use 25 therms or less, you get charged $0.6686/therm. If you use more than the 25, you get charged a higher rate for every therm above the initial 25, $0.8587/therm.
25 therms
So in a month where we use 25 therms, we pay the monthly charge of $8.80, plus the therm charge, which is:
And so for the month we pay:
45 therms
We know how much it costs for 25 therms - we've included the monthly charge and the therm charge (I'll use the unrounded figure here - no sense in giving the gas company an extra half cent!). And so what we need to know is the charge for the extra 20 therms. That's:
This gives us:
Function
This is a step function where