a solar water heater costs about $5400 to install (after rebates).

Question

A traditional gas water heater costs about $900, and costs about $400 per year to run. The average annual cost to run the solar water heater is about $80. Create total cost functions for each of the water heaters as a function of the number of years that it is used, and graph these functions on the same set of axes. How many years would you need to use a solar water heater in order for the total cost to become less than the total cost of the gas water heater?

Answer 1

For the traditional water heater, we have the initial cost plus the annual cost, so T(t) = 900 + 400t, for t years.

For the solar water heater, we have only the annual cost, so S(t) = 80t.

 

The second part of the question is very strange.  With the given information, the solar water heater costs less from the first year.  Is there an initial cost to the solar water heater that you did not include?