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. Further suppose that the number of cars driven on 1st Avenue can be modeled by an exponential function, C= p * a t (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 50 and 100; 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 the 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.
Do NOT use the same values for “p” and “a” as another student in the class.
This is "college"? This was a standard assignment for ALG II students in the exponential decay section.
So what is your question? Choose p (I suggest 100), and a. You need at least one value of a <1 (decay), and a couple of values above 1, (growth).
I would graph them also with your graphing calculator.
Please put your subject in the subject box, terms like "college", "adult", are meaningless to our answering volunteers, and is a waste of their time trying to seek out their subject questions.
sorry but yes it is college algebra
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. Further suppose that the number of cars driven on 1st Avenue can be modeled by an exponential function, C= p * a t (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.
Step 1 is to choose a value for “q” between 50 and 100; this is the initial number of cars on the road.
Step 2 is to choose a value for “z”; this is the growth factor – you can choose “z” to be any number between 0 and 1 “OR” choose “z” to be any number greater than 1.
1) Insert the chosen values for “q” and “z” into the formula listed above.
2) Use the formula to find the number of cars, C, on 1st Avenue at any three values of time, t, in days that you want.
3) Provide a written summary of your results explaining context of the problem. Would you want to commute to work each day on this road?
How to I solve this problem using the number 75 for Q & 2 for Z?
The model given to you was
Cars=OriginalNumber*(growth factor)t
In the steps, Q is the original number
z is the growth factor
t is time in days.
I'm very confused?
Step 1: Choose a value for "p"
Let's choose p = 75. This means that initially, there are 75 cars on the road.
Step 2: Choose a value for "a"
We can choose a value for "a" between 0 and 1 or a value greater than 1. Let's choose a = 0.8. This means that the number of cars on the road decreases over time.
Now we can proceed to answer the questions.
1) Inserting the values for "p" and "a" into the formula:
C = p * a^t
C = 75 * 0.8^t
2) Finding the number of cars, C, on 1st Avenue at three values of time, t:
Let's choose t = 0, 1, and 6 as our time values.
For t = 0:
C = 75 * 0.8^0 = 75 * 1 = 75 cars
For t = 1:
C = 75 * 0.8^1 = 75 * 0.8 = 60 cars
For t = 6:
C = 75 * 0.8^6 = 75 * 0.262144 = 19.6078 cars (rounded to 4 decimal places)
So, at time t = 0, there are 75 cars on 1st Avenue. After 1 day (t = 1), the number of cars decreases to 60. After 6 days (t = 6), the number of cars further decreases to approximately 19.6078.
3) Written summary of results and decision on commuting to work:
In the context of the problem, the number of cars on 1st Avenue decreases exponentially over time with the chosen values of "p" and "a". Initially, there are 75 cars, but this number decreases as time progresses. For example, after 6 days, there are only approximately 19.6078 cars on the road.
Based on these results, commuting to work on this road would be preferred if you dislike heavy traffic. Since the number of cars decreases over time, you would encounter fewer cars and potentially experience smoother and faster commuting. However, if you prefer a busy road with more cars, this road might not be desirable for daily commuting.