Concept explainers
a.
To write: a recursive rule for the number
a.
Answer to Problem 53E
Explanation of Solution
Given:
The number of initial members in an online music service is
And the company continuously loses 20% of the member and gain 5000 new members.
Calculation:
According to the question, the company loses 20% of its members each year, 80% remain in the company from one year to the next. Also 5,000 are acquired each year.
Hence, a recursive rule for the number
b.
To find: the number of members at the start of the 5th year.
b.
Answer to Problem 53E
Explanation of Solution
Given:
The number of initial members in an online music service is
And the company continuously loses 20% of the member and gain 5000 new members.
Calculation:
From part (a)
Therefore, start of the 5th year is
Hence, the number of members at the start of the 5th year is
c.
To describe: what happens to the number of members over time.
c.
Answer to Problem 53E
Explanation of Solution
Given:
The number of initial members in an online music service is
And the company continuously loses 20% of the member and gain 5000 new members.
Calculation:
From part (a)
Observe that the numbers of the company approach 25,000. Over time, the number stabilizes at about 25,000 people.
Hence, the number of members over time is
Chapter 8 Solutions
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