Question 294000: 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 , (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
Part2: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!
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! (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
Part2: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.
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Let a = 10000 homes ; Let p = 1.10 (10% growth rate)
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1) Insert the chosen values for p and a into the formula listed above.
N(t) = 10,0000*(1.1)^t
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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!
Let t = 1 yr, Then t = 5 yrs, Then t = 20 years
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If t = 1, N(1) = 10,000*1.1 = 11,000 homes after one year
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If t = 5, N(5) = 10,000(1.1)^5 = 16,105 homes after 5 years
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If t = 20, N(20) = 10,000(1.1)^20 = 67275 homes after 20 years
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Cheers,
Stan H.
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Cheers,
Stan H.
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