1. 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 hours = 2.5 kilowatt-hours. Suppose the power use of a customer over a 30-day period is given by the continuous function P = ft), 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-day period, and explain why your Riemann sum is an approximation of the desired property. B. Derive an expression representing the total number of kilowatt-hours used by the customer in the 30-day period, and explain your reasoning. (This expression should not be an approximation.) C. Consider the following table of data for the function (t). At) 2.3 1 2.5 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 (t) represents the number of kilowatts being used by a customer at time i 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.
1. 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 hours = 2.5 kilowatt-hours. Suppose the power use of a customer over a 30-day period is given by the continuous function P = ft), 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-day period, and explain why your Riemann sum is an approximation of the desired property. B. Derive an expression representing the total number of kilowatt-hours used by the customer in the 30-day period, and explain your reasoning. (This expression should not be an approximation.) C. Consider the following table of data for the function (t). At) 2.3 1 2.5 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 (t) represents the number of kilowatts being used by a customer at time i 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.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
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Transcribed Image Text:1. 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 · hours = 2.5 kilowatt-hours.
Suppose the power use of a customer over a 30-day period is given by the continuous
function P = f(1), 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-day period, and explain why your Riemann sum is an approximation of
the desired property.
B. Derive an expression representing the total number of kilowatt-hours used by the
customer in the 30-day period, and explain your reasoning. (This expression should not be
an approximation.)
C. Consider the following table of data for the function f(t).
2.3
1
2.5
2
2.1
3
3.9
4
3.6
5.5
4.5
7
5.6
8
1.2
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.
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