Chapter 8.1, Problem 26E

a.

To determine

To integrate B(x)over the interval $\left[-0.5,10.5\right]$ to find the bagel sales for 11 years.

Answer to Problem 26E

The bagel sales for 11 year is approximately 799 thousands

Explanation of Solution

Given information:

The interval of the integration is $\left[-0.5,10.5\right]$

Calculation:

Integrate B(x)over the interval $\left[-0.5,10.5\right]$

  $\begin{array}{l}={\displaystyle \underset{-0.5}{\overset{10.5}{\int }}(1.6x^2+2.3x+5})dx\\ ={\left[\frac{1.6}{3}{x}^3+\frac{2.3}{2}{x}^2+5x\right]}_{-0.5}^{10.5}\\ ={\left[0.533x^3+1.15x^2+5x\right]}_{-0.5}^{10.5}\\ \approx 799\end{array}$

Therefore,

The bagel sales for 11 year is approximately 799 thousands

b.

To determine

To explain graphically why the answer in part (a) is better than the answer in 25 (c).

Answer to Problem 26E

The answer in (a) corresponds to the interval $\left[-0.5,10.5\right]$ and the answer in 25(c) corresponds to the interval [0, 11] and the lower limit of integration used in part (a) is closer to the extremum than that of in 25(c), hence the answer in part (a) is better than the answer in 25 (c).

Explanation of Solution

Given information:

Answer in part (a) is 797.5 thousands

Answer in part (c) is 904.02 thousands

The graph of the function is

  

The answer in (a) corresponds to the interval $\left[-0.5,10.5\right]$ and the answer in 25(c) corresponds to the interval [0, 11] and the lower limit of integration used in part (a) is closer to the extremum than that of in 25(c), hence the answer in part (a) is better than the answer in 25 (c).