Chapter 4.8, Problem 23E

(a)

To determine

To write: A model that relates the attendance in millions as a function of the number of years since 1985.

Answer to Problem 23E

  $f\left(x\right)=0.02x^3-0.46x^2+3.94x+47.49$

Explanation of Solution

Given information: Baseball: The attendance at major league baseball games for various years is listed below.

  

Calculation:

  

  

  $f\left(x\right)=0.02x^3-0.46x^2+3.94x+47.49$

(b)

To determine

To predict:the year when attendance will reach 100 million, using the model.

Answer to Problem 23E

  $2000$

Explanation of Solution

Given information: Baseball: The attendance at major league baseball games for various years is listed below.

  

Calculation:

  $\begin{array}{l}f\left(x\right)=71\\ 71=0.02x^3-0.46x^2+3.94x+47.49\\ 0.02x^3-0.46x^2+3.94x-23.51=0\end{array}$

  

.

  $\begin{array}{l}1985+15=2000\\ \Rightarrow 2000\end{array}$

(c)

To determine

To find: whether the attendance for 1998 follow your model or not and do you think the race to break the homerun record affected attendance.

Answer to Problem 23E

  $\text{No}$

Explanation of Solution

Given information: Baseball: The attendance at major league baseball games for various years is listed below.

  

Calculation:

1998 is 13 years from 1985

  $\begin{array}{l}f\left(13\right)=0.02{\left(13\right)}^3-0.46{\left(13\right)}^2+3.94\left(13\right)+47.49\\ f\left(13\right)=64.91\end{array}$

No, since we’re speaking in millions, the model isn’t close to the actual attendance.

As such, the homerun race did affect the attendance.