A gas company has the following rate schedule for natural gas usage in single-family residences:
Monthly service charge
Per therm service charge 1st 25 therms
Over 25 therms
$8.80
$0.6686/therm $0.85870/therm
What is the charge for using 25 therms in one month? Show your work. What is the charge for using 45 therms in one month? Show your work. Construct a function that gives the monthly charge C for x therms of gas.
If you mean,
Monthly service charge: $8.80
Per therm service charge 1st 25 therms: $0.6686/therm
Over 25 therms: $0.85870/therm
therefore for the first 25 therms in a month,
8.80 + 0.6686(25) = ?
and for 45 therms in a month,
8.80 + 0.6686(25) + 0.85870(45-25) = ?
For x therms in a month,
Between zero and 25:
f(x) = 8.80 + 0.6686x for 0 ≤ x ≤ 25
Greater than 25:
f(x) = 8.80 + 0.6686(25) + 0.85870(x-25) for x > 25
Just simplify this function.
hope this helps~ `u`
Thank you !!
To find the charge for using 25 therms in one month, we need to multiply the per therm service charge by the number of therms used.
Given:
Per therm service charge for the first 25 therms = $0.6686/therm
So, the charge for using 25 therms = 25 therms * $0.6686/therm = $16.715
To find the charge for using 45 therms in one month, we need to consider two different rates: one for the first 25 therms and another for the remaining therms.
Given:
Per therm service charge for the first 25 therms = $0.6686/therm
Per therm service charge for over 25 therms = $0.85870/therm
For the first 25 therms, the charge = 25 therms * $0.6686/therm = $16.715
For the remaining therms (45 therms - 25 therms = 20 therms), the charge = 20 therms * $0.85870/therm = $17.174
So, the total charge for using 45 therms = $16.715 + $17.174 = $33.889
Now, let's construct a function that gives the monthly charge C for x therms of gas:
For x ≤ 25 therms,
C(x) = Monthly service charge + (Per therm service charge * x)
For x > 25 therms,
C(x) = Monthly service charge + Per therm service charge for the first 25 therms + (Per therm service charge for over 25 therms * (x - 25))
Note: We don't have the value of the monthly service charge, so we cannot provide an exact function. The monthly service charge needs to be given in order to construct the complete function.
To find the charge for using 25 therms in one month, we need to multiply the per therm service charge for the first 25 therms by the number of therms.
The per therm service charge for the first 25 therms is $0.6686/therm. So, we multiply $0.6686/therm by 25 therms:
Charge for 25 therms = $0.6686/therm × 25 therms = $16.715
Therefore, the charge for using 25 therms in one month is $16.715.
To find the charge for using 45 therms in one month, we need to consider the per therm service charge for the first 25 therms and the over 25 therms charge.
For the first 25 therms, we calculate the charge as we did before:
Charge for the first 25 therms = $0.6686/therm × 25 therms = $16.715
For the remaining 20 therms (45 therms - 25 therms), we need to use the over 25 therms charge, which is $0.85870/therm. So, we multiply $0.85870/therm by 20 therms:
Charge for the additional 20 therms = $0.85870/therm × 20 therms = $17.174
Now, we add the two charges together:
Total charge for 45 therms = Charge for the first 25 therms + Charge for the additional 20 therms = $16.715 + $17.174 = $33.889
Therefore, the charge for using 45 therms in one month is $33.889.
To construct a function that gives the monthly charge C for x therms of gas, we can use the following piecewise function:
C(x) = 8.80 + 0.6686 * x, if 0 <= x <= 25
C(x) = 8.80 + 0.85870 * (x - 25), if x > 25
This function takes into account the monthly service charge of $8.80 and the different per therm service charges based on whether x is within the first 25 therms or above that limit.