Chapter 12.3, Problem 65E

Inflation The following graph shows the approximate value of the U.S. Consumer Price Index (CPI) from July 2005 through March 2006:

$I\left(t\right)$

CPI July 2005-Mar 2006

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The approximating curve shown on the figure is given by

$I\left(t\right)=0.06t^3-0.8t^2+3.1t+195\left(0\le t\le 8\right),$

where t is time in months since the start of July 2005.

a. Use the model to estimate the monthly inflation rate in December 2005 and February $\left(t=5\text{ and }t=7\right)$.

b. Was inflation slowing or speeding up in February 2006?

c. When was inflation speeding up? When was inflation slowing? [HINT: See Example 3.]