Chapter 5.3, Problem 64E

Inflation The following graph shows the approximate value of the U.S. Consumer Price Index (CPI) from September 2004 through November 2005:

$I\left(t\right)$

CPI Sep 2004-Nov 2005

The approximating curve shown on the figure is given by

$I\left(t\right)=-0.005t^3+0.12t^2-0.01t+190\left(0\le t\le 14\right),$

where t is time in months since the start of December 2004.

a. Use the model to estimate the monthly inflation rate in July 2005 $\left(t=10\right)$. [Recall that the inflation rate is $I^{\prime }\left(t\right)/I\left(t\right)$.]

b. Was inflation slowing or speeding up in July 2005?

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