HERE COMES THE SUN
© Mathalicious 2014
HERE COMES THE SUN
name date
Are solar panels worth the cost?
Act One: You Are My Sunshine 1 The average American home uses 910 kilowatt-‐hours (kWh) of electricity each month. For your state, find the
average price of a kilowatt-‐hour. At this rate, how much would you expect to pay the electricity company (aka the electrical utility) over a year? Over ten years? Twenty?
2 Instead of buying electricity from the local utility company, some people install solar panels to power their homes. Ten years ago, a system designed to generate 1000 kWh each month cost $100,000. Assuming monthly electricity usage stayed the same, how long would someone need to own the panels to justify the cost?
3 Today, a 1000-‐kWh system costs around $50,000, but the government pays 30% of this through its Residential Efficiency Property Credit. How long would it take to pay this off now, and do you think it’s a smart investment?
4 If you want solar power but don’t want to invest $50,000, you have another option: lease solar panels. A company will install them for around $3,000, and you pay a monthly $80 fee. However, you no longer get the government rebate, and typically have to commit to a 20-‐year agreement. Write an equation for the total cost of each option below, and graph them. For what number of months is each one the cheapest?
Electric Utility
Solar (Buy)
Solar (Lease)
Total Cost ($)
Optimal Months
2
Act Two: House of the Rising Sun 5 Solar systems are designed to generate a certain amount of electricity each month. If you use more than your
capacity, you can buy additional electricity from the utility company at the regular rate. If you use less, you can actually sell remaining electricity back to the utility at the wholesale rate (typically around $0.05 per kWh). For each scenario below, calculate how much you’d expect to spend in total on electricity over m months, and determine for what number of months each plan will be the cheapest now. (For simplicity, let’s assume that the cost of installing solar panels is the same regardless of their capacity.) cap. = 1000 kWh usage = 1400 kWh
cap. = 1300 kWh usage = 910 kWh
Electric Utility
Solar (Buy)
Solar (Lease)
Cost ($)
Optimal
Cost ($)
Optimal
6 When you opt for solar power, you decide how large of a system to install. You also decide how much electricity
to use each month. For each electricity option, write an expression for the total cost as a function of months; let u represent your month electrical usage, and let s represent the solar system’s capacity.
Total Cost ($)
Electric Utility
Solar (Buy)
Solar (Lease)
Usage > Cap.
Usage = Cap.
Usage < Cap.
7 More people are turning to renewable energies like solar, and the technology is getting cheaper and more efficient. What effect do you expect this will have on factors such as installation and rental costs, capacity, electricity rates, etc., and how do you think this will influence people’s electricity decisions in the coming years?
3
Total Cost
$70,000
$60,000
$50,000
$40,000
$30,000
$20,000
$10,000
$0 0
100
200
300
400
500
600 Number of Months
