Question 108055: Can you pleasecheck my answer>
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
I picked 20 homes the first year and thought that "a" should then be 365
H=20*1^365
H=20*1
H=20
Thank You
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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.
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H(t) = p*a^t
If you pick 0 < a < 1 the number of houses built decreases as time increases:
For example:
If a = (1/2), H(3) = p*(1/2)^3 = (1/8)p---number built in the 3rd yr.
If a + (1/2), H(5) = p*(1/2)^5 = (1/32)p---number built in the 5th yr.
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If you pick a>1 the number of houses built increases as time increases:
for example:
If a = 2, H(3) = p*2^3 = 8p---number built in the 3rd yr.
If a = 2, H(5) = p*2^5 = 32p---number built in the 5th yr.
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It is up to you to determine whether you want the number of houses to
increase or decrease. Good luck.
Cheers,
Stan H.
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