1.)A utility company has the following rate schedule for natural gas usage in a city’s business district:
Monthly service charge: $8.80
Per therm service charge
1st 25 therms : $0.6686/therm
Over 25 therms: $0.85870/therm
(a) What is the charge for using 25 therms in one month?
(b) What is the charge for using 45 therms in one month?
(c) Construct a function that gives the monthly charge C for x therms of gas.
I am totally lost, can someone please show me how to do this???
is using x therms,
f(x) = 8.80 + .6686x for 0<=x<=25
25 therms cost $16.715, so
f(x) = 8.80+16.715 + .85870x
= 25.515 + .85870x for 25<x
now just plug in values for x, using the appropriate function
what do you mean when you say, "the appropriate function?" what function are you referring to?
I mean to where I have to graph the following function using transformations. And have to be sure to graph all of the stages on 1 graph. Then I have to state the domain and range.
f(x) = 8.80+0.6686x for 0 < x <= 25
f(x) = 25.515+0.85870(25-x) for x > 25
Sure! Let's break it down step-by-step.
(a) To calculate the charge for using 25 therms in one month, we need to consider both the monthly service charge and the per therm service charge.
The monthly service charge is given as $8.80.
For the per therm service charge, we have two tiers:
- For the first 25 therms, the rate is $0.6686/therm.
- For any additional therms beyond 25, the rate is $0.85870/therm.
Since we are only considering 25 therms, we are within the first tier.
So, the charge for using 25 therms in one month is calculated by multiplying the number of therms (25) by the per therm service charge for the first tier:
Charge for 25 therms = 25 therms * $0.6686/therm
(b) Similarly, for using 45 therms in one month, we need to consider both the monthly service charge and the per therm service charge.
Again, the monthly service charge is $8.80.
This time, we have 25 therms in the first tier and an additional 20 therms in the second tier. So, we need to calculate the charge for each tier separately and add them together:
Charge for the first 25 therms = 25 therms * $0.6686/therm
Charge for the additional 20 therms = 20 therms * $0.85870/therm
Total charge for 45 therms = Charge for the first 25 therms + Charge for the additional 20 therms
(c) To construct a function that gives the monthly charge C for x therms of gas, we need to consider the monthly service charge and the per therm service charge for each tier based on the given rate schedule.
The function can be defined as follows:
C(x) = Monthly service charge + Charge for the first x therms in the first tier + Charge for any additional therms beyond x in the second tier
For the first tier, if x is greater than 25, the charge will be:
Charge for the first x therms = 25 therms * $0.6686/therm
For the second tier, if x is greater than 25, the charge will be:
Charge for any additional therms beyond x = (x - 25) therms * $0.85870/therm
The monthly charge C for x therms of gas is then:
C(x) = Monthly service charge + Charge for the first x therms + Charge for any additional therms beyond x