Concept explainers
(a)
To explain: The sequence that models the amount
(a)
Explanation of Solution
Formula to calculate the amount of pollutants at the end of the nth year is,
Since, the rate of pollutants which are expelled is 70%. Thus the rate of pollutants which are not expelled is
Assume
The amount of pollutants at the end of the nth year is
Amount of chemical present in the lake at the beginning time is 2400 tons.
The recursive sequence that models the amount
Hence, the sequence that models the amount
(b)
To find: The first five terms of the sequence
(b)
Answer to Problem 5P
The first five terms of the sequence
Explanation of Solution
Calculation:
Since the initial amount of pollutants present in the lake at the beginning is 2400 tons. Thus,
Substitute 1 for
Substitute 2 for
Substitute 3 for
Substitute 4 for
Hence, the first five terms of the sequence
(c)
To find: The formula for
(c)
Answer to Problem 5P
The value of
Explanation of Solution
Calculation:
Since, the terms
The general term
Since
The sum of the geometric sequence is,
Substitute
Substitute
Hence, the value of
(d)
To find: The pollutants remain in the lake after 6 year and after a long time.
(d)
Answer to Problem 5P
The pollutants remain in the lake after 6 year is
Explanation of Solution
Calculation:
For the pollutants remains in the lake after 6 year, substitute 6 for n in equation (3) to evaluate
For the pollutants remains in the lake after a long time, substitute
Hence, the pollutants remain in the lake after 6 year is
(e)
To sketch: The graph of the given equation
(e)
Explanation of Solution
The value of
Substitute some values of n and find the corresponding values of the function as given below in the table,
0 | 2400 |
1 | 2472 |
2 | 2474.16 |
3 | 2474.22 |
4 | 2474.23 |
5 | 3427.82 |
6 | 3427.82 |
7 | 3427.82 |
8 | 3727.82 |
Table
Plot the points in the graph and connect the points.
From the above figure, it can be observed that as the value of n increases in
Chapter 12 Solutions
Precalculus: Mathematics for Calculus - 6th Edition
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