Answered: Use the model to estimate the monthly…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

The following graph shows the approximate value of the United States Consumer Price Index (CPI) from December 2006 through July 2007.

On the graph titled "CPI Dec 2006-July 2007," the horizontal axis is labeled t and the vertical axis is labeled I(t). The curve begins at the point (0, 202), goes up and right becoming more steep, passes through the approximate point (3.5, 205.5), goes up and right becoming less steep, and ends at the approximate point (7, 208.7).

The approximating curve shown on the figure is given by

I(t) = −0.04t³ + 0.4t² + 0.1t + 202 (0 ≤ t ≤ 7),

where t is time in months since the start of December 2006.

(a)

Use the model to estimate the monthly inflation rate in January 2007 (t = 1).

Recall that the inflation rate is

I′(t)

I(t)

(Round your answer to three decimal places.)

(b)

Was inflation slowing or speeding up in January 2007?

slowing downspeeding up