A real estate developer builds a small number of model homes, one each in a different style. During an open house event, there i
s a lot of interest, but prospective buyers almost exclusively prefer the "Model C" style. At the conclusion of the open house event, the developer begins ramping up production quickly, doubling the number of "Model C" houses completed each month. While she does not tear them down, she decides not to build more of the other 5five styles of houses. In the month when the first residents begin to move in, two hundred sixty one total houses have been built, including the original model homes. I need to write an equation to model the number of houses built over time. It has to be in y=a * b^x-k + h form, but there doesn't have to be all of them.
The number of new houses doubles each month, so the base (b) is that multiplier, 2. Then x is the number of months since the construction started (presumably at the end of the open house). If you want x to be something else, then h needs to be chosen so that (x -k) is the number of months the doubling has been taking place.
The value h represents the initial build of 5 houses. This is confirmed by the number 261 = 256 + 5 = 2^8 +5.
So, your equation for the number of houses built over time is ...
