Concept explainers
A puppy weighs 0.85 lb at birth, and each week he gains 24% in weight. Let an be his weight in pounds at the end of his nth week of life.
- (a) Find a formula for an.
- (b) How much does the puppy weigh when he is 6 weeks old?
- (c) Is the sequence a1, a2, a3, … arithmetic, geometric, or neither?
(a)
To find: The formula for
Answer to Problem 13T
The formula of the sequence generated is
Explanation of Solution
Given:
The weight of puppy at birth is
Calculation:
As there is an increment of weight every week of
Substitute
Thus, formula of
(b)
To find: Weight of puppy after 6 weeks.
Answer to Problem 13T
Weight of puppy after 6 weeks is
Explanation of Solution
Given:
The weight of puppy at birth is
Calculation:
From part (a) the formula of the sequence generated is,
Substitute 6 for n in equation (1) for the weight of puppy after 6 weeks,
Thus, the weight of puppy after 6 weeks is
(c)
Whether the sequence
Answer to Problem 13T
The sequence
Explanation of Solution
The sequence to be in arithmetic should have the common difference between two specific term constant with nature linear, for geometric should have common ratio between two specific term constant with nature geometric.
From part (a) the formulae of the sequence generated is,
Substitute 1 for n in equation (1) for first term of sequence.
Substitute 2 for n in equation (1) for second term of sequence.
Substitute 3 for n in equation (1) for third term of sequence.
The common ratio for first two terms is,
The common ratio for second and third terms is,
From the above result the value of
Thus, the sequence
Chapter 12 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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