Chapter 12.3, Problem 66E

Inflation The following graph shows the approximate value of the U.S. Consumer Price Index (CPI) from March 2006 through May 2007.

$I\left(t\right)$

CPI Mar 2006-May 2007

The approximating curve shown on the figure is given by

$I\left(t\right)=0.02t^3-0.38t^2+2t+200\left(0\le t\le 14\right),$

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

a. Use the model to estimate the monthly inflation rate in September 2006 and January 2007 $\left(t=6\text{ and }t=10\right)$.

b. Was inflation slowing or speeding up in January 2007?

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