Americans are addicted to electricity. We need it to power everything from our cell phones to our big-screen TVs. But all that juice doesn’t come for free, and while many tout renewable energy as the future, it can be expensive. So, are technologies like solar panels worth the cost?

In this lesson, students set up and solve systems of linear equations to compare different electricity plans. They learn about the costs associated with buying solar panels, leasing solar panels, and sticking with their local utilities, and determine when each option is the least expensive. They also make predictions about how these costs might change in the future.

### Students will

• Use proportions to calculate the cost of an electricity bill over one, ten, and twenty years
• Construct linear models for the total cost of purchasing electricity from various sources
• Compare the cost of buying solar panels to the cost of buying electricity from the local utility
• Solve linear systems to determine the least expensive option between buying solar panels, leasing solar panels, and buying electricity from the local utility
• Discuss how the cost of electricity (from renewable and non-renewable sources) may change in the future

### Before you begin

Students should be able to write and graph a linear equation (e.g. if something costs \$3000 to set up an \$80 per month to run, then over m months you will have spent \$3000 + \$80m in total). Some previous experience solving systems of linear equations will also be helpful.