Chapter 5.3, Problem 63E

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

$I\left(t\right)$

CPI Dec 2006-July 2007

The approximating curve shown on the figure is given by

$I\left(t\right)=-0.04t^3+0.4t^2+0.1t+202\left(0\le t\le 7\right),$

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

a. Use the model to estimate the monthly inflation rate in February 2007 $\left(t=2\right)$. [Recall that the inflation rate is $I^{\prime }\left(t\right)/I\left(t\right)$.]

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

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