B. 24*30 = 720 hours so the energy used is
∫[0,720] P(t) dt
A. You can approximate that using n intervals, each of width h = 720/n
by the Right-hand sum
n
∑ P(720/n) * h
k=1
C. Use n=10
Power companies typically bill customers based on the number of kilowatt-hours used during a single billing period. A kilowatt is a measure of how much power (energy) a
customer is using, while a kilowatt-hour is one kilowatt of power being used for one hour.
For constant power use, the number of kilowatt-hours used is calculated by kilowatt-hours=kilowatts * time (in hours). Thus, if customers use 5 kilowatts for 30 minutes, they'll have used 5 kilowatts * (1/2)hrs =2.5 kilowatt-hours.
Suppose the power use of a customer over a 30-day period is given by the continuous
function P(t) where P is kilowatts, t is time in hours, and t =0 corresponds to the
beginning of the 30 day period.
A.
Approximate, with a Riemann sum, the total number of kilowatt-hours used by the customer in the 30 days. Please tell sigma notation, and exact approximation.
B.
Derive an expression representing the total number of kilowatt-hours used by the
customer in the 30-day period. (This expression should not be an approximation.)
C. Consider the following data for the function.
t f(x)
0 2.3
1 2.5
2 2.1
3 3.9
4 3.6
5 5.5
6 4.5
7 5.6
8 1.2
9 1.0
10 1.8
Recall that f(t) represents the number of kilowatts being used by a customer at time t hours from the beginning of the billing period. Estimate the number of kilowatt-hours the customer uses in this 10-hour period, and explain your method.
2 answers
Please elaborate B and C.
2 answers