Lina is considering installing solar panels on her house. Solar Advantage offers to install solar panels that generate 390 kWh of electricity per month for an installation fee of **$14,000**. She uses **450 kWh** of electricity per month, and her local utility company charges **20¢ per kWh**.(a) If Lina gets all her electrical power from the local utility company, find a linear function $ U $ that models the cost $ U(x) $ (in dollars) of electricity for $ x $ months of service.\[ U(x) = \](b) If Lina has Solar Advantage install solar panels on her roof that generate 390 kWh of power per month, find a linear function $ S $ that models the cost $ S(x) $ (in dollars) of electricity for $ x $ months of service.\[ S(x) = \](c) Determine the number of months it would take to reach the break-even point for installation of Solar Advantage's solar panels, that is, determine when $ S(x) = U(x) $. (Round your answer to the nearest month.)\[ \text{months} \]

Name: Lina is considering installing solar panels on her house. Solar Advan
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: Lina is considering installing solar panels on her house. Solar Advantage offers to install solar panels that generate 390 kWh of electricity per month for an installation fee of **$14,000**. She uses **450 kWh** of electricity per month, and her lo

Answered: Lina is considering installing solar…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Concept explainers

Topic Video

Question

Lina is considering installing solar panels on her house. Solar Advantage offers to install solar panels that generate 390 kWh of electricity per month for an installation fee of **$14,000**. She uses **450 kWh** of electricity per month, and her local utility company charges **20¢ per kWh**.

(a) If Lina gets all her electrical power from the local utility company, find a linear function $ U $ that models the cost $ U(x) $ (in dollars) of electricity for $ x $ months of service.

\[ U(x) = \]

(b) If Lina has Solar Advantage install solar panels on her roof that generate 390 kWh of power per month, find a linear function $ S $ that models the cost $ S(x) $ (in dollars) of electricity for $ x $ months of service.

\[ S(x) = \]

(c) Determine the number of months it would take to reach the break-even point for installation of Solar Advantage's solar panels, that is, determine when $ S(x) = U(x) $. (Round your answer to the nearest month.)

\[ \text{months} \]

Expert Solution

Step 1

Step:- 1

Given that charges for electricity per month by local utility company = 20 cents per kWh

uses of electricity per month = 450 kWh

solar panel generate electricity = 390 kWh

one installation fee = $14,000

1 dollar = 100 cents

Step:- 2

Part (a)

$\cos t U (x) f o r 1 k W h f o r 1 m o n t h = 20 c e n t s \cos t U (x) f o r 450 k W h f o r 1 m o n t h = 20 \times 450 \cos t U (x) f o r 450 k W h f o r x m o n t h = (20 \times 450 \times x) c e n t s \cos t U (x) f o r 450 k W h f o r x m o n t h = $ (20 \times 450 \times x) \times \frac{1}{100} = $ 90 x \cos t U (x) f o r 450 k W h f o r x m o n t h = $ 90 x \cos t U (x) = $ 90 x$

Step:- 3

Part (b)

$s o l a r p a n e l g e n e r a t e p o w e r = 390 k W h L i n a u s e s p o w e r = 450 E x t r a p o w e r u s e d b y L i n a = (450 - 390) = 60 k W h \cos t f o r x m o n t h S (x) = (20 \times 60 \times x) \times \frac{1}{100} + 14, 000 \cos t f o r x m o n t h S (x) = (12 x + 14, 000) S (x) = $ (12 x + 14, 000)$

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Discrete Probability Distributions$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Similar questions