Suppose that the number of cars, C, on 1st Avenue in acity over a period of time

Question

Suppose that the number of cars, C, on 1st Avenue in acity over a period of time t, in months, is graphed on arectangular coordinate system where time is on the horizontal axis.Suppose that the number of cars driven on 1st Avenue can be modeledby an exponential function, C= p *at(C=p*a^t)where p is the number of cars on the road on thefirst day recorded. If you commuted to work each day along 1stAvenue, would you prefer that the value of "a" be between0 and 1 or larger than 1? Explain your reasoning.
Suppose that the number of cars, C, on 1st Avenue in acity over a period of time t, in months, is graphed on arectangular coordinate system where time is on the horizontal axis.Suppose that the number of cars driven on 1st Avenue can be modeledby an exponential function, C= p *at(C=p*a^t)where p is the number of cars on the road on thefirst day recorded. If you commuted to work each day along 1stAvenue, would you prefer that the value of "a" be between0 and 1 or larger than 1? Explain your reasoning.

Explanation / Answer

First, recognize that the value of t will always be aninteger since it is a number of months. Now, if you commute to workevery day on 1st avenue, clearly you'd want C to decrease over timerather than increase. As t increases, C willeither increase of decrease, depending on what the value ofa. Hint: try two different values of a, forexample .5 and 2, try them each with increasing values oft and see if they increase or decrease.

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