Blog Post #2- Jean Marcel

Blog Post #2

a. Find a real world application OR design your own experimental application relating to rates of change.

The real world application I chose is the value of a car during 10 years. The initial value of the car is $22,000 and as year passes it depreciates in value.

b. Write a narrative or synopsis explaining your application/experiment and include a question.

My experiment is how car depreciate in value as it ages in years. Starting with an initial value of $22,000 in year 0 and it keeps depreciating as time passes, but it is only measured in a time lapse of 10 years. Would it reach the point where the car has no value? 

c. Create a table of values for the data that you have recorded from your application/experiment.

d. Graph the points using the data from your table of values (connect the dots). 

    

         e.  Calculate the slope (ARC) of at least three secant lines originating from the same point on your graph to three different points on your graph (i.e. maybe you want to know what happens exactly at x = 20, so your points might be (20, 62), (20, 56), (20, 50)).  Explain what you notice about the ARC of these secant lines and what the calculations mean/represent in terms of your experiment/application. According to the three secant lines the value keeps growing in a negative growth, meaning that the car keeps losing value with time.

      

      f.  Sketch an approximation of a tangent line that passes though the same point (P) from part e to which you connected your secant lines (i.e. you would draw a tangent line through the point 20, since that is the same point that you used to calculate your three different secant lines)

   

     g. Choose a second point (Q) on the tangent line, and calculate the slope of the line (PQ). This calculation will be the instantaneous rate of change ((IRC or derivative at a point)…be sure to identify the units correctly).  Explain what this calculation means mathematically and in terms of your experiment/application.

       (6770-16200)/ (9-1)= -9930/8 (aprox. -1241.25) 

       This mean that at that particular point and time the car is going to have a depreciation of -1241.25.

      h. Explain in detail how you know that the value from part g is the IRC. (i.e. since the values of calculations from part d are getting smaller and smaller, this shows that the slope of the secant is getting closer and closer to the tangent line … or some explanation similar to this). BE DETAILED!!! The IRC is the change at a given moment and according to part d the number are growing in negative values. The IRC proves that the depreciation value is growing in a negative way showing us that the car depreciates depending on the year.