# Commuter choices

Suppose that the number of cars, C, on 1st Avenue in a city over a period of time t, in days, is graphed on a rectangular coordinate system where time is on the horizontal axis. Further suppose that the number of cars driven on 1st Avenue can be modeled by an exponential function, C=p*a^t where p is the number of cars on the road on the first day recorded and t is the number of days.

You are going to decide how you would prefer to commute to work each day.

Step 1 is to choose a value for "p" between 100 and 200; this is the initial number of cars on the road.

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.

1) Insert the chosen values for "p" and "a" into the formula listed above.

2) Use the formula to find number of cars, C, on 1st Avenue, at any three values of time, t, in days that you want. Show your calculations and put units on your final answer.

3) Provide a written summary of your results explaining them in the context of the original problem. Would you want to commute to work each day on this road? Explain why or why not.

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#### Solution Summary

Commuter choices are depicted.