- Solve applied problems involving rational functions.
- Solve rational inequalities.
Home Solar Panel Efficiency Analysis
Jake recently installed a solar panel system on his Phoenix home and wants to optimize its performance. His daily energy efficiency [latex]E(h)[/latex] (as a percentage of maximum theoretical output) depends on the number of peak sunlight hours [latex]h[/latex] according to:
[latex]E(h) = \frac{90h - 180}{h + 4}[/latex]
Solar Efficiency Analysis
Jake’s goal is to achieve at least 60% efficiency to make his monthly electricity bill negative (meaning he sells more energy back to the grid than he uses). This means he needs to solve the rational inequality:
How to: To test signs in rational inequalities:
- Pick a test point from each relevant interval
- Substitute into the simplified expression
- Determine if the result is positive or negative
- Include intervals where the expression satisfies the inequality