Show all work neatly and legibly. Equation is; y= 378.1e^0.0668x a. If this mode
ID: 2891675 • Letter: S
Question
Show all work neatly and legibly.
Equation is; y= 378.1e^0.0668x
a. If this model remains accurate,what will the outstanding consumer credit be in 2013?
b. Use you rmodel topredict the year in which consumer credit reach $6000billion.
c. At what rate is the consumer credit changing in 2015. Discuss, and find the derivative as a rate of change.
UNIT 4-Google Docs PROJECT MAT 1033 The table shows outstanding consumer credit (in billions of dollars) at the beginning of various years. where x 0 is year 1980. oar Credit (in billions) 1980 1985 1990 1995 2000 2005 2010 10 15 20 25 30 350.5 524.0 797.7 1010.4 1543.7 2200.1 2438.7 Source: U. S. Federal Reserve. (1) Using Microsoft Excel, graph a scatter diagram of the data with year, x, as the independent variable and credit, y, as the dependent variable. Label your axes and give your graph a title. (2) Based on the scatter diagram drawn in (1) decide which mathematical model (linear, quadratic, exponential, or logarithmic) best describes the relationship between year and credit. Give justification to your choice of model by giving a full explanation. (3) Using Trendline in Excel, find the model of best fit, and graph it on the scatter diagram from (1). Be sure you label your Trendline and show the equation on the graph. (4) Write a function of the best fit model in (3). (5) Show all work neatly and legibly a. If this model remains accurate, what will the outstanding consumer credit be in 2013? b. Use your model to predict the year in which consumer credit reach $6000 billion. (6) At what rate is the consumer credit changing in 2015. Discuss, in complete sentences based on your understanding of your work on items 1-5 and of the derivative as a rate of change. You may need to refer to sections covered in class where we have discussed linear, quadratic, exponential, or logarithmic modeling. (Sections: 2.2, 2.3, 3.3, 3.4, 4.1-4.4, 11.3-11.8). MacBook AirExplanation / Answer
y= 378.1e^(0.0668x)
x = 0 is 1980
So, 2013 is x = 33
So,
y= 378.1e^(0.0668*33)
y = 3427.41 billion
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b)
6000 = 378.1e^(0.0668x)
e^(0.0668x) = 6000/378.1
e^(0.0668x) = 15.8688177730759058
0.0668x = ln(15.8688177730759058)
x = 41.3825754088818095603
So, x = 41, i.e approx 2021
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c)
Deriivng :
y' = 378.1 * e^(0.0668x) * 0.0668
y' = 25.25708e^(0.0668x)
In 2015, x = 35 :
y' = 25.25708e^(0.0668*35)
y' = 261.6758
So, it is increasing at 261.6758 bn dollars per year in 2015