21.Application: A solar panel is used to power an overhead sign on a highway. Ench square metre of solar panel receives about 200 W of solar power. This solar panel converts about 15% of the solar energy to electrical power. (a) Write a function for the solar power, S(A) measured in watts (W) for any given area, A in square metres. (b) Write a function for the total electrical power. P(S) in watts (W) this solar panel can generate. (c) How large must the solar panel be if the sign uses 6 W of electrical energy?

## Step 1: Define the solar power function### The solar power, , is 200 W per square meter. Therefore, for an area in square meters, the total solar power received is watts.## Step 2: Define the electrical power function### The solar panel converts 15% of the solar energy to electrical power. So, if is the solar power in watts, the electrical power is given by .## Step 3: Combine the functions and solve for the required area### We can express the electrical power as a function of the area by substituting into : . The sign requires 6W of electrical power, so we set and solve for : , which gives square meters.