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Algebra - Algebra Word Problem
Expert: Scott A Wilson - 11/4/2009
Question
Suppose that the number of cars, C, on 1st Avenue in a city over a period of time t, in months, is graphed on a rectangular coordinate system where time is on the horizontal axis. Suppose that the number of cars driven on 1st Avenue can be modeled by an exponential function, C= p * at (C=p*a^t) where p is the number of cars on the road on the first day recorded. If you commuted to work each day along 1st Avenue, would you prefer that the value of "a" be between 0 and 1 or larger than 1? I don't even know where to start. Thank you advance for your help.
Answer
Since the equation we are given is C = p•a^t, the value of a needs to be less than one for the function to return smaller values as time goes on.
Using a spreadsheet and exporting the data to you,
I will show you the effect if a = 0.95 and a=1.05.
This is a^t where t is 1, 2, 3, 4, 5, ... 98, 99, 100.
As can be seen, 0.95 decreases where 1.05 increases.
You might think of this as being one means you get the whole thing again.
Being slightly greater than 1 means giving you a little more than 1.
Being less than 1 means we're taking away just a little and not quite giving back the whole.
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