Chapter 8.1, Problem 38E

To determine

ToFind:

Tofind the annual inflation rate for $12$ month period running from the middle of the first month to the middle of the last month.

Answer to Problem 38E

The overall inflation rate is calculated to be $40thousandths$ .

Explanation of Solution

Given information:

The following table shows the monthly inflation rate for energy prices for thirteen consecutive months.

  

Formula:

The area of an individual trapezoidal is $=\frac{1}{2}\left(b_1+b_2\right)\Delta x$

From given $n=12$ , $\Delta x=1$ ,

The area each and every month is calculated to be the summation of all the months,

  $\begin{array}{l}A=\frac{1}{2}\left(3.6+4.0\right)+\frac{1}{2}\left(4.0+3.1\right)+\frac{1}{2}\left(3.1+2.8\right)+\frac{1}{2}\left(2.8+2.8\right)\\ \frac{1}{2}\left(2.8+3.2\right)+\frac{1}{2}\left(3.2+3.3\right)+\frac{1}{2}\left(3.3+3.1\right)+\frac{1}{2}\left(3.1+3.2\right)+\frac{1}{2}\left(3.2+3.4\right)\\ \frac{1}{2}\left(3.4+3.9\right)+\frac{1}{2}\left(3.9+4.0\right)\\ A=\frac{1}{2}\left(7.6+7.1+5.9+6.0+6.5+6.4+6.3+\mathrm{6.6.}+6.8+7.3+7.9\right)\\ A=\frac{1}{2}\left(80\right)=40\end{array}$

Therefore, the overall inflation rate is calculated to be $40thousandths$ .