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Math Help - exponential

  1. #1
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    exponential

    Part 1: 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 , where p is the number of new homes built in the first year recorded. If you were a homebuilder looking for work, would you prefer that the value of a to be between 0 and 1 or larger than 1? Explain your reasoning.
    Typing hint: Type formula above as H = p * a^t
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  2. #2
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    Quote Originally Posted by harry View Post
    Part 1: 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 , where p is the number of new homes built in the first year recorded. If you were a homebuilder looking for work, would you prefer that the value of a to be between 0 and 1 or larger than 1? Explain your reasoning.
    Typing hint: Type formula above as H = p * a^t
    Umm. Why the hint? Is that not supposed to be the model eponential function?
    The given model, H = p*at, is not exponential.

    Say, H = p * a^t -----(i)

    If you are looking for work, you need more new houses to be built. So you need H to increase as time t goes on.

    If 0 < a < 1, or "a" is a fraction less than 1, then as t increases, the a^t decreases in value. So H decreases too. No good for you.
    Example, a = 0.3
    at t=1, a^t = (0.3)^1 = 0.3
    at t=2, a^t = (0.3)^2 = 0.09 <----less than 0.3
    at t=3, a^t = (0.3)^3 = 0.027 <---less than 0.09


    If "a" is greater than 1, then the a^t increases as t increases. So the H increases too. Good for you.
    Example, a = 3
    at t=1, a^t = (3)^1 = 3
    at t=2, a^t = (3)^2 = 9 <----more than 3
    at t=3, a^t = (3)^3 = 27 <---more than 9

    So which one you prefer?
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