Chapter 12.3, Problem 46E

a.

To determine

To find the first ten terms of the model.

Answer to Problem 46E

  $\frac{1}{8}D$

Explanation of Solution

Given:

The given sequence model is $a_n=17.3032181{(0.864605)}^n$ , for $n=1,2,\mathrm{3....}$

Calculation:

Substituting the value of $n=1,2,\mathrm{3....}$ in the sequence $a_n=17.3032181{(0.864605)}^n$ , the ten terms obtained are

  $\begin{array}{l}{a}_1=30.0\\ a_2=26.8\\ a_3=23.1\\ a_4=20.0\\ a_5=17.3\end{array}$             $\begin{array}{l}{a}_6=15.0\\ a_7=12.9\\ a_8=11.2\\ a_9=9.7\\ a_{10}=8.4\end{array}$

b.

To determine

To estimate the number of students during the $1995-1996$ school year.

Answer to Problem 46E

  $a_n=D{\left(\frac{1}{8}\right)}^{n-1}$

Explanation of Solution

Given:

The given sequence model is $a_n=17.3032181{(0.864605)}^n$ , for $n=1,2,\mathrm{3....}$

Calculation:

For $1995-1996$ , the value of $n=9$

  $a_9=9.7$

In the actual graph the average number of students having to share a

computer during the 1995-1996 school year is 10. The estimated value is very close to this $\left(9.7\right).$ Thus we can conclude that the estimated sequence model is almost correct.

c.

To determine

To make a prediction for the average number of students for 2006-2007 school year.

Answer to Problem 46E

  $\frac{8}{7}D$

Explanation of Solution

Given:

The given sequence model is $a_n=17.3032181{(0.864605)}^n$ , for $n=1,2,\mathrm{3....}$

Calculation:

For $2006-2007$ , the value of $n=14$

  $\begin{array}{l}$ a_{14}=17.3032181{(0.864605)}^{14}$$ a_n=17.3032181{(0.864605)}^n$a_{14}=4.7\end{array}$

The average number of students per computer for the

2000-2001 school year is $4.7$ .

d.

To determine

To find out whether the sequence approach the limit.

Answer to Problem 46E

  $0$

Explanation of Solution

Given:

The given sequence model is $a_n=17.3032181{(0.864605)}^n$ , for $n=1,2,\mathrm{3....}$

Calculation:

Yes, the sequence approaches towards zero when the value of $n$ increases and tends to infinity.

e.

To determine

To find out whether realistically the students will reach this limit.

Answer to Problem 46E

No.

Explanation of Solution

Given:

The given sequence model is $a_n=17.3032181{(0.864605)}^n$ , for $n=1,2,\mathrm{3....}$

Calculation:

NO. Realistically, the student computer ratio will never reach this limit.

Because when each student have separate computer the ratio will become 1:1.