8th Edition

ISBN: 9781337904285

Author: Larson

Publisher: CENGAGE L

Concept explainers

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 …

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experime…

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Question

Chapter 8.1, Problem 130E

To determine

To write: a recursive sequence that gives the population $pn$ of trout in the lake in terms of the year n, with n = 0 corresponding to 2020.

Expert Solution

Answer to Problem 130E

The recursive sequence that gives the population $pn$ of trout in the lake in terms of the year n is: $Pn=0.75Pn−1+500.$

Explanation of Solution

Given information: A landlocked lake has been selected to be stocked in the year 2020

with 5500 trout and to be restocked each year thereafter with 500 trout. Each year the fish population declines 25% due to harvesting as well as natural causes.

Calculation:

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

$P0=5500.Pn=0.75Pn−1+500.$

To determine

To find: the numbers of trout in the lake for n = 1, 2, 3 and 4 and interpret these values in the context of the situation.

Expert Solution

Answer to Problem 130E

In 2021, there will be $P1=4625 fish.$

In 2022, there will be $P2=3969 fish.$

In 2023, there will be $P3=3477fish.$

In 2024, there will be $P4=3107 fish.$

Explanation of Solution

Given information: $Pn=0.75Pn−1+500.$

Calculation:

In 2021, there will be $P1=0.75P0+500=0.75×5500+500=4625 fish.$

In 2022, there will be $P2=0.75P1+500=0.75×4625+500=3969 fish.$

In 2023, there will be $P3=0.75P2+500=0.75×3969+500=3477fish.$

In 2024, there will be $P4=0.75P3+500=0.75×3477+500=3107 fish.$

To determine

To find: the number of trout as time passes infinitely using a graphing utility and explains.

Expert Solution

Answer to Problem 130E

2000 trout.

Explanation of Solution

Given information: $Pn=0.75Pn−1+500.$

Calculation:

$∑p=0∞0.75Pn−1+500=2000 trout.$ As time passes, the population of trout decreases at a decreasing rate. Because the population is growing smaller and still declines 25 %, each time 25% is taken from a smaller number there is a smaller decline in the number of trout.

Chapter 8.1, Problem 129E

Chapter 8.1, Problem 131E

Chapter 8 Solutions

PRECALCULUS W/LIMITS:GRAPH.APPROACH(HS)

Ch. 8.1 - Prob. 1E Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - Prob. 7E Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

Ch. 8.1 - Prob. 11E Ch. 8.1 - Prob. 12E Ch. 8.1 - Prob. 13E Ch. 8.1 - Prob. 14E Ch. 8.1 - Prob. 15E Ch. 8.1 - Prob. 16E Ch. 8.1 - Prob. 17E Ch. 8.1 - Prob. 18E Ch. 8.1 - Prob. 19E Ch. 8.1 - Prob. 20E Ch. 8.1 - Prob. 21E Ch. 8.1 - Prob. 22E Ch. 8.1 - Prob. 23E Ch. 8.1 - Prob. 24E Ch. 8.1 - Prob. 25E Ch. 8.1 - Prob. 26E Ch. 8.1 - Prob. 27E Ch. 8.1 - Prob. 28E Ch. 8.1 - Prob. 29E Ch. 8.1 - Prob. 30E Ch. 8.1 - Prob. 31E Ch. 8.1 - Prob. 32E Ch. 8.1 - Prob. 33E Ch. 8.1 - Prob. 34E Ch. 8.1 - Prob. 35E Ch. 8.1 - Prob. 36E Ch. 8.1 - Prob. 37E Ch. 8.1 - Prob. 38E Ch. 8.1 - Prob. 39E Ch. 8.1 - Prob. 40E Ch. 8.1 - Prob. 41E Ch. 8.1 - Prob. 42E Ch. 8.1 - Prob. 43E Ch. 8.1 - Prob. 44E Ch. 8.1 - Prob. 45E Ch. 8.1 - Prob. 46E Ch. 8.1 - Prob. 47E Ch. 8.1 - Prob. 48E Ch. 8.1 - Prob. 49E Ch. 8.1 - Prob. 50E Ch. 8.1 - Prob. 51E Ch. 8.1 - Prob. 52E Ch. 8.1 - Prob. 53E Ch. 8.1 - Prob. 54E Ch. 8.1 - Prob. 55E Ch. 8.1 - Prob. 56E Ch. 8.1 - Prob. 57E Ch. 8.1 - Prob. 58E Ch. 8.1 - Prob. 59E Ch. 8.1 - Prob. 60E Ch. 8.1 - 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Prob. 56CR Ch. 8 - Prob. 57CR Ch. 8 - Prob. 58CR Ch. 8 - Prob. 59CR Ch. 8 - Prob. 60CR Ch. 8 - Prob. 61CR Ch. 8 - Prob. 62CR Ch. 8 - Prob. 63CR Ch. 8 - Prob. 64CR Ch. 8 - Prob. 65CR Ch. 8 - Prob. 66CR Ch. 8 - Prob. 67CR Ch. 8 - Prob. 68CR Ch. 8 - Prob. 69CR Ch. 8 - Prob. 70CR Ch. 8 - Prob. 71CR Ch. 8 - Prob. 72CR Ch. 8 - Prob. 73CR Ch. 8 - Prob. 74CR Ch. 8 - Prob. 75CR Ch. 8 - Prob. 76CR Ch. 8 - Prob. 77CR Ch. 8 - Prob. 78CR Ch. 8 - Prob. 79CR Ch. 8 - Prob. 80CR Ch. 8 - Prob. 81CR Ch. 8 - Prob. 82CR 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

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a recursive sequence that gives the population p n of trout in the lake in terms of the year n, with n = 0 corresponding to 2020.

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To write: a recursive sequence that gives the population pn<m:math><m:mrow><m:msub><m:mi>p</m:mi><m:mi>n</m:mi></m:msub></m:mrow></m:math> of trout in the lake in terms of the year n, with n = 0 corresponding to 2020.

Answer to Problem 130E

Explanation of Solution

To find: the numbers of trout in the lake for n = 1, 2, 3 and 4 and interpret these values in the context of the situation.

Answer to Problem 130E

Explanation of Solution

To find: the number of trout as time passes infinitely using a graphing utility and explains.

Answer to Problem 130E

Explanation of Solution

Chapter 8 Solutions

To write: a recursive sequence that gives the population $pn$ of trout in the lake in terms of the year n, with n = 0 corresponding to 2020.