Suppose that the number of new homes built, H, in a city over a period of time, t, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of homes built can be modeled by an exponential function, H= p * at , (H = p*a^t) where p is the number of new homes built in the first year recorded, and t is the number of years. You are going to decide if you would like to be a homebuilder in this market.
Step 1 is to choose a value for “p” between 100 and 200; this is the initial number of homes built.
Step 2 is to choose a value for “a”; this is the growth factor – you can choose “a” to be any number between 0 and 1 “OR” choose “a” to be any number greater than 1. Do not choose 0 or 1, as these are trivial cases.
1) Insert the chosen values for “p” and “a” into the formula listed above.
2) Use the formula to find the number of homes built, H, at any three values of time, t, in years that you want. Show your calculations and put units on your final answer!
3) Provide a written summary of your results explaining them in the context of the original problem. If you were a homebuilder, would you be interested in continuing to build homes in this market over the long run? Explain why or why not.
Do NOT use the same values for “p” and “a” as another student in the class. Be sure to reference your sources using APA style.