electricity costs 7.57 a month plus 8.77 per kilo watt hour for the first 400 kWhr and 6.574 per kWhr for all useage over 400 in a month.
what is the cost for 300 kWhr? 2638 What is the cost of 700? 7.57+8.77 times 400 and 6.574 times 300? 5487.77 I think. I need to write a piecewise function x= kWhr used per month and c=cost of useage. please help me I do not understand
To write a piecewise function for calculating the cost of electricity usage based on the number of kilowatt hours (kWhr) used per month, we need to establish the two separate price brackets: one for usage up to 400 kWhr, and another for usage over 400 kWhr.
Let's break it down step by step:
1. For usage up to 400 kWhr:
- The cost per kWhr is given as $8.77.
- So, the cost for the first 400 kWhr would be: 400 kWhr * $8.77/kWhr = $3508.
2. For usage exceeding 400 kWhr:
- The cost per kWhr is given as $6.574.
- To calculate the cost for usage over 400 kWhr, we subtract the initial 400 kWhr from the total usage amount.
- So, for any usage (x) above 400 kWhr, the cost can be calculated as: (x - 400) kWhr * $6.574/kWhr.
Now, let's combine both scenarios to create the piecewise function:
c(x) = $7.57/month + $8.77/kWhr * x, if 0 < x ≤ 400
c(x) = $7.57/month + $8.77/kWhr * 400 + $6.574/kWhr * (x - 400), if x > 400
Using this function, we can calculate the cost for different usage scenarios:
1. For 300 kWhr:
Here, 300 kWhr ≤ 400 kWhr, so we use the first part of the piecewise function.
c(300) = $7.57 + $8.77/kWhr * 300
Plugging in the numbers, we get: c(300) = $7.57 + $2631 = $2638.
2. For 700 kWhr:
Here, 700 kWhr > 400 kWhr, so we use the second part of the piecewise function.
c(700) = $7.57 + $8.77/kWhr * 400 + $6.574/kWhr * (700 - 400)
Plugging in the numbers, we get: c(700) = $7.57 + $3508 + $13.148 * 300 = $5487.77.
Therefore, the cost for 300 kWhr is $2,638, and the cost for 700 kWhr is $5,487.77, as you correctly calculated.