Concept explainers
Fitness Program Sheila decides to embark on a swimming program as the best way to maintain cardiovascular health. She begins by swimming 5 min on the first day, then adds
- (a) Find a recursive formula for the number of minutes Tn that she swims on the nth day of her program.
- (b) Find the first 6 terms of the sequence Tn.
- (c) Find a formula for Tn. What kind of sequence is this?
- (d) On what day does Sheila attain her goal of swimming at least 65 min a day?
- (e) What is the total amount of time she will have swum alter 30 days?
(a)
The recursive sequence that models the number of minutes
Answer to Problem 2P
The recursive sequence that models the number of minutes
Explanation of Solution
Given:
Sheila swims 5 min on the first day and
Formula used:
Formula to calculate the amount at the end of the nth day is,
Calculation:
Shelia swims 5 min on the first day that is
Assume
Hence, the recursive sequence that models the number of minutes
(b)
The first six terms of the sequence
Answer to Problem 2P
The first six terms of the sequence
Explanation of Solution
Given:
Sheila swims 5 min on the first day and
Calculation:
The value of
Substitute 2 for
Substitute 3 for
Substitute 4 for
Substitute 5 for
Substitute 6 for
Hence, the first six terms of the sequence
(c)
The formula and behavior of sequence
Answer to Problem 2P
The formula of sequence
Explanation of Solution
Formula used:
Formula to calculate the nth term of the arithmetic sequence
Given:
Sheila swims 5 min on the first day and
Calculation:
Since, the common difference of the sequence
Substitute
Hence, the formula of sequence
(d)
The number of days when Sheila attain her goal for at least 65 min.
Answer to Problem 2P
Sheila attain her goal for at least 65 min in 41 days.
Explanation of Solution
Given:
Sheila swims 5 min on the first day and
Calculation:
Sheila attain her goal for at least 65 min that is
Substitute
Hence, Sheila attain her goal for at least 65 min in 41 days.
(e)
The total amount of time after 30 days.
Answer to Problem 2P
The total amount of time after 30 days is
Explanation of Solution
Given:
Sheila swims 5 min on the first day and
Calculation:
Substitute
Hence, the total amount of time after 30 days is
Chapter 12 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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