Precalculus with Limits: A Graphing Approach

7th Edition

ISBN: 9781305071711

Author: Ron Larson

Publisher: Brooks/Cole

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Question

Chapter 8.1, Problem 123E

(a)

To determine

To write: a recursive sequence that given the population $pn$ of trout in the lake in terms of the year $n$ , with $n=0$ corresponding to 2015.

(a)

Expert Solution

Answer to Problem 123E

The recursive sequence that gives the population of trout in the lake in terms of year $n$ is:

$pn=(0.75)Pn−1+500$

Explanation of Solution

Given information:

A landlocked lake has been selected to be stocked in the year 2015 with 5500 trout, and to be restocked given year thereafter with 500 trout. Given year the fish population declines 25%duw to harvesting and other natural causes.

Calculation:

The recursive sequence that gives the population of trout in the lake in terms of year $n$ is:

$P0=5500pn=(0.75)Pn−1+500$

(b)

To determine

To find: the numbers of trout in the lake for $n=1,2,3$ and 4.

(b)

Expert Solution

Answer to Problem 123E

The numbers of trout in the lake are:

4625, 3969, 3477, 3108

Explanation of Solution

Given information:

Calculation:

To find the numbers of trout in the lake, substitute $n=1,n=2,n=3,n=4$ in the sequence one by one.

$P1=(0.75)P1−1+500=(0.75)(5500)+500=4625P2≈3969P3≈3477P4≈3108$

Thus, the numbers of trout in the lake are:

4625, 3969, 3477, 3108

These values represent the number of trout in the lake for the years 2016 through 2019.

(c)

To determine

To find: the number of trout in the lake as time passes infinitely using graphing utility.

(c)

Expert Solution

Answer to Problem 123E

The number of trout in the lake is found as 2000 trout.

Explanation of Solution

Given information:

Calculation:

Using graphing utility, the number of trout in the lake is found as 2000 trout.

As time passes the population of trout decreases at a decreasing rate. Because the population is growing smaller and still decline 25%, each time 25% is taken from a smaller number, there is a smaller decline in the number of trout.

Chapter 8.1, Problem 122E

Chapter 8.1, Problem 124E

Chapter 8 Solutions

Precalculus with Limits: A Graphing Approach

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Prob. 40RE Ch. 8 - Prob. 41RE Ch. 8 - Prob. 42RE Ch. 8 - Prob. 43RE Ch. 8 - Prob. 44RE Ch. 8 - Prob. 45RE Ch. 8 - Prob. 46RE Ch. 8 - Prob. 47RE Ch. 8 - Prob. 48RE Ch. 8 - Prob. 49RE Ch. 8 - Prob. 50RE Ch. 8 - Prob. 51RE Ch. 8 - Prob. 52RE Ch. 8 - Prob. 53RE Ch. 8 - Prob. 54RE Ch. 8 - Prob. 55RE Ch. 8 - Prob. 56RE Ch. 8 - Prob. 57RE Ch. 8 - Prob. 58RE Ch. 8 - Prob. 59RE Ch. 8 - Prob. 60RE Ch. 8 - Prob. 61RE Ch. 8 - Prob. 62RE Ch. 8 - Prob. 63RE Ch. 8 - Prob. 64RE Ch. 8 - Prob. 65RE Ch. 8 - Prob. 66RE Ch. 8 - Prob. 67RE Ch. 8 - Prob. 68RE Ch. 8 - Prob. 69RE Ch. 8 - Prob. 70RE Ch. 8 - Prob. 71RE Ch. 8 - Prob. 72RE Ch. 8 - Prob. 73RE Ch. 8 - Prob. 74RE Ch. 8 - Prob. 75RE Ch. 8 - Prob. 76RE Ch. 8 - Prob. 77RE Ch. 8 - Prob. 78RE Ch. 8 - Prob. 79RE Ch. 8 - Prob. 80RE Ch. 8 - Prob. 81RE Ch. 8 - Prob. 82RE Ch. 8 - Prob. 83RE Ch. 8 - Prob. 84RE Ch. 8 - Prob. 85RE Ch. 8 - Prob. 86RE Ch. 8 - Prob. 87RE Ch. 8 - Prob. 88RE Ch. 8 - Prob. 89RE Ch. 8 - Prob. 90RE Ch. 8 - Prob. 91RE Ch. 8 - Prob. 92RE Ch. 8 - Prob. 93RE Ch. 8 - Prob. 94RE Ch. 8 - Prob. 95RE Ch. 8 - Prob. 96RE Ch. 8 - Prob. 97RE Ch. 8 - Prob. 98RE Ch. 8 - Prob. 99RE Ch. 8 - Prob. 1CT Ch. 8 - Prob. 2CT Ch. 8 - Prob. 3CT Ch. 8 - Prob. 4CT Ch. 8 - Prob. 5CT Ch. 8 - Prob. 6CT Ch. 8 - Prob. 7CT Ch. 8 - Prob. 8CT Ch. 8 - Prob. 9CT Ch. 8 - Prob. 10CT Ch. 8 - Prob. 11CT Ch. 8 - Prob. 12CT Ch. 8 - Prob. 13CT Ch. 8 - Prob. 14CT Ch. 8 - Prob. 15CT Ch. 8 - Prob. 16CT Ch. 8 - Prob. 17CT Ch. 8 - Prob. 18CT Ch. 8 - Prob. 19CT Ch. 8 - Prob. 20CT Ch. 8 - Prob. 21CT Ch. 8 - Prob. 22CT Ch. 8 - Prob. 23CT Ch. 8 - Prob. 24CT Ch. 8 - Prob. 25CT Ch. 8 - Prob. 26CT

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