(a) Explanation Given Information: The graph showing the approximate value of the U.S. consumer Price Index (CPI) from March 2006 through May 2007 is provided below, The equation of the curve is, I ( t ) = 0.02 t 3 − 0.38 t 2 + 2 t + 200 Here, t is in months and t = 0 represents March 2006 . Formula Used: The quadratic formula for the equation of the form a x 2 + b x + c = 0 is, x = − b ± b 2 − 4 a c 2 a Derivative formula, d d x ( x n ) = n x n − 1 d d x ( constant ) = 0 Where, n is any real number. Calculation: Consider the graph, And, the equation, I ( t ) = 0.02 t 3 − 0.38 t 2 + 2 t + 200 Here, t is in months and t = 0 represents March 2006 . Now, as it can be observed that there is no t intercept in the graph but there is y intercept at I ( 0 ) = 200 . Thus, it indicates that CPI was never zero during the period shown in graph and in March 2006 , the CPI was 200 . Now, obtain the derivative of the provided equation of curve, I ′ ( t ) = d d t ( 0.02 t 3 − 0.38 t 2 + 2 t + 200 ) = d d t ( 0.02 t 3 ) − d d t ( 0.38 t 2 ) + d d t ( 2 t ) + d d t ( 200 ) = 0.02 × 3 t 2 − 0.38 × 2 t + 2 + 0 = 0.06 t 2 − 0.76 t + 2 Now, to obtain stationary points, set I ′ ( t ) = 0 , 0 = 0.06 t 2 − 0.76 t + 2 Now, use the quadratic formula to obtain the value of t , t = 0.76 ± 0.76 2 − 4 ( 0.06 ) ( 2 ) 2 ( 0.06 ) Thus, t = 0.76 + 0.76 2 − 4 ( 0.06 ) ( 2 ) 2 ( 0.06 ) ≈ 3.7 Also, t = 0.76 − 0.76 2 − 4 ( 0.06 ) ( 2 ) 2 ( 0.06 ) ≈ 8.9 Now, substitute 3.7 for t in the equation I ( t ) = 0.02 t 3 − 0.38 t 2 + 2 t + 200 , I ( 3.7 ) = 0.02 ( 3.7 ) 3 − 0.38 ( 3.7 ) 2 + 2 ( 3.7 ) + 200 = 203.2 Also, substitute 8.9 for t in the equation I ( t ) = 0.02 t 3 − 0.38 t 2 + 2 t + 200 , I ( 3 (b) To determine The characteristic of inflation rate from the stationary extrema of the provided curve,

Finite Mathematics and Applied Calculus (MindTap Course List)

7th Edition

ISBN: 9781337274203

Author: Stefan Waner, Steven Costenoble

Publisher: Cengage Learning

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Chapter 12.4, Problem 36E

(a)

To determine

To calculate: The intercept, points of inflection and extrema of the curve in terms of CPI.

Also, interpret the features in terms of CPI if the graph provided is,

(b)

To determine

The characteristic of inflation rate from the stationary extrema of the provided curve,

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Chapter 12 Solutions

Finite Mathematics and Applied Calculus (MindTap Course List)

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The intercept, points of inflection and extrema of the curve in terms of CPI. Also, interpret the features in terms of CPI if the graph provided is,

Solution Summary: The graph shows the approximate value of the U.S. consumer price index (CPI) from March 2006 through May 2007.

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To calculate: The intercept, points of inflection and extrema of the curve in terms of CPI. Also, interpret the features in terms of CPI if the graph provided is,

The characteristic of inflation rate from the stationary extrema of the provided curve,

Chapter 12 Solutions

To calculate: The intercept, points of inflection and extrema of the curve in terms of CPI.

Also, interpret the features in terms of CPI if the graph provided is,