## Real World Applications – Algebra I

### Topic

How much energy could solar panels save for homeowners?

### Student Exploration

For this activity, you will need a graphing calculator.

Hook: Watch this video:

Below is a table representing the annual savings on the electricity bill for a homeowner in Los Angeles, CA with a 5.5-kilowatt photovoltaic solar panel system. This system offsets 95% of the homeowner’s electricity use. With electricity rates increasing a certain percentage every year, the homeowner’s savings increased as well.

Year | Annual Savings |
---|---|

2010 | $1,175.35 |

2011 | $1,245.87 |

2012 | $1,320.62 |

2013 | $1,399.86 |

2014 | $1,483.85 |

2015 | $1,572.88 |

2016 | $1,667.26 |

2017 | $1,767.29 |

2018 | $1,873.33 |

2019 | $1,985.73 |

2020 | $2,104.87 |

2021 | $2,231.17 |

- Do you think this data represents a linear, exponential or quadratic relationship? Why?
- Plot this table in your graphing calculator and create a scatter plot. What are some observations you can make about the data points?
- Determine the exponential regression line that fits this data. Write down the equation, and round to the nearest tenth.
- What is the initial value? What do you think this means in relation to this situation?
- What is the growth factor for this exponential equation? What do you think this represents in relations to this situation?

- Using your graph, what do you think the homeowner’s savings will be in 2030? Why? How did you find your answer? Does it make sense?

### Resources Cited

http://energy.gov/energysaver/energy-saver

### Connections to other CK-12 Subject Areas

#### Earth Science

- same hook