5. James is considering installing solar panels on his home in Colorado to save on electricity costs and contribute to renewable energy. The total cost for purchasing and installing the solar panels is $18,000. Colorado offers a state tax incentive of $3,000, and the federal government provides a tax credit of 26% of the total cost. James expects to save $150 per month on his electricity bills if he installs the new system.
(a) Calculate the effective cost of the solar panels after applying the incentives.
(b) Write a linear equation to represent the total savings $S$ from the solar panels after $t$ years.
(c) Determine how long it will take for James to break even on his investment. Round your answer to two decimal places.