Chapter 7.5, Problem 3P

Solution

To identify: What happens to the number of members over time if online music service loses 8% of its current members and adds 1200 new members each year. Use the graphing method and algebraic method.

The number of members over the time approaches to $15000$ .

Given information:

Online music service loses 8% of its current members and adds 1200 new members each year.

Explanation:

Consider the given information.

Online music service loses 8% of its current members and adds 1200 new members each year.

Let they have 100% members at the starting then after losing 8% members, company have 92% member left and 1200 new members join each year.

So, the rule can be written as:

  $a_n=0.92a_{n-1}+1200$

Assume that the sequence has a limit L , which is the value that the sequence approaches as n becomes large.

As n become larger the left-hand side approaches to L while the value of the right-hand side approaches to $0.92L+1200$ .

  $\begin{array}{c}L=0.92L+1200\\ 0.08L=1200\\ L=15000\end{array}$

The sequence approaches to the limit $L=15000$ .

Now solve this graphically.

Step 1: Open Ti-83 calculator press MODE key select Seq and Dot option.

  

Step 2: Press Y= key and enter the given sequence. Press the key $\text{X,T,θ,n}$ to write n .

  

Step 3: Press GRAPH key.

  

The sequence approaches to the limit $L=15000$ .