An increasing number of businesses and homeowners are installing solar panels to harness the sun's energy. The U.S. Department of Energy projects that the solar cell usage, in millions of kilowatt-hours in the United States, can be modeled by the function S(t) = 0.73t^2 + 15.8t + 2.7, where t represents the number of years after 2000. What was the projected solar cell usage in 2001? And in 2002?

 To find the projected solar cell usage in 2001 and 2002, we will use the function S(t) = 0.73t^2 + 15.8t + 2.7, where t represents the number of years after 2000.

For the year 2001, which is 1 year after 2000, we'll set t = 1: S(1) = 0.73(1)^2 + 15.8(1) + 2.7 = 0.73 * 1 + 15.8 * 1 + 2.7 = 0.73 + 15.8 + 2.7 = 19.23 million kilowatt-hours.

For the year 2002, which is 2 years after 2000, we'll set t = 2: S(2) = 0.73(2)^2 + 15.8(2) + 2.7 = 0.73 * 4 + 15.8 * 2 + 2.7 = 2.92 + 31.6 + 2.7 = 37.22 million kilowatt-hours.

Therefore, the projected solar cell usage for the year 2001 was 19.23 million kilowatt-hours, and for the year 2002, it was 37.22 million kilowatt-hours.

Extra: The use of solar panels is a way to convert solar energy—a renewable energy source—into electrical energy that can be used to power homes, businesses, and various other applications. Solar panels are composed of many solar cells, also known as photovoltaic cells, which convert sunlight directly into electricity.

Solar energy is one of the leading forms of renewable energy that is growing in adoption due to its low environmental impact and its potential to help reduce reliance on fossil fuels, which are finite resources that contribute to climate change.

The mathematical model provided by the U.S. Department of Energy in the form of S(t) is a quadratic equation. It is likely derived from past data on solar cell usage and projections based on factors such as technological improvements, cost reductions, policy incentives, and market trends. Quadratic models are useful because they can account for acceleration in growth or uptake over time, which is typical in the adoption of new technologies. As time progresses, you would normally see a rising curve in the graph of S(t) vs. t, indicating increasing usage of solar power, which reflects real-world observations.