Question 159131: 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?
Assistance is requested with the equation ... below is what has been done.
When p > 0, a > 1, t gets larger, as well as y. When 0 < a < 1, then y gets continually smaller. As a homebuilder seeking work, the preference would be to have the value of a to larger than 1 (a > 1) to ensure plenty of work.
H=500 t = 1 p = 5
f(x)/t = p*ln(a)*a^t
y/1 = 5 (1) * 1^1
1^1 = 2.72^1 (1)
(1) (2.72^1)/ 1
(1) 2.72* 1
y = 2.72
Thank you for the assistance.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Assistance is requested with the equation ... below is what has been done.
When p > 0, a > 1, t gets larger, as well as y. When 0 < a < 1, then y gets continually smaller. As a homebuilder seeking work, the preference would be to have the value of a to larger than 1 (a > 1) to ensure plenty of work.
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The equation is H = p*a^t
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You are correct in saying that H is an increasing function when a>1 and
a decreasing function when 0 < a < 1, like (1/2).
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I'm not sure what you are trying to do with the equation after that:
H=500 t = 1 p = 5
f(x)/t = p*ln(a)*a^t
y/1 = 5 (1) * 1^1
1^1 = 2.72^1 (1)
(1) (2.72^1)/ 1
(1) 2.72* 1
y = 2.72
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It appears you are letting t = 1 and p = 5 and H = 500
If so you should get:
500 = 5*a^1
500 = 5a
a = 100
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Cheers,
Stan H.
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