Chapter 11.5, Problem 47PPS

(a)

To determine

Enter ${\text{x}}_{\text{0}}$ in the cell A1 of your spread sheet. Enter “ = $(0.3)·\text{A1}+5000$ ” in cell A2.

Answer to Problem 47PPS

  $\text{Cell}\text{A2}=11,000$

Explanation of Solution

Given:

Consider the sequence with ${\text{x}}_{\text{0}}=20000\text{and}\text{f(x)}=0.3\text{x}+5000$

Enter ${\text{x}}_{\text{0}}$ in the cell A1 of your spread sheet. Enter “ = $(0.3)·\text{A1}+5000$ ” in cell A2.

Concept Used:

Enter ${\text{x}}_{\text{0}}$ in the cell A1 of your spread sheet. Enter “ = $(0.3)·\text{A1}+5000$ ” in cell A2.

Calculation:

  $x_0=20000\text{and}f(x)=0.3x+5000$

  $\begin{array}{l}\text{Cell}\text{A1}=x_0=20000\\ \text{Cell}\text{A2}=(0.3)·\text{A1}+5000=0.3··20,000+5000=11,000\end{array}$

Thus, $\text{Cell}\text{A2}=11,000$

(b)

To determine

Copy cell A2, highlight cells A3 through A70, and paste. What do you notice about the sequence?

Answer to Problem 47PPS

It converges to 7142.857.

Explanation of Solution

Given:

Consider the sequence with ${\text{x}}_{\text{0}}=20000\text{and}\text{f(x)}=0.3\text{x}+5000$

Copy cell A2, highlight cells A3 through A70, and paste. What do you notice about the sequence?

Concept Used:

Copy cell A2, highlight cells A3 through A70, and paste. What do you notice about the sequence?

It converges to 7142.857.

Thus, it converges to 7142.857.

(c)

To determine

How do spreadsheets help analyze recursive sequence?

Answer to Problem 47PPS

They make it easier to analyze recursive sequence because they can produce the first 100 terms instantaneously; it would take a long time to calculate the terms by hand.

Explanation of Solution

Given:

Consider the sequence with ${\text{x}}_{\text{0}}=20000\text{and}\text{f(x)}=0.3\text{x}+5000$

How do spreadsheets help analyze recursive sequence?

Concept Used:

They make it easier to analyze recursive sequence because they can produce the first 100 terms instantaneously; it would take a long time to calculate the terms by hand.