Textbook ExpertVerified Tutor
30 Dec 2021
Given information
We are given the formula :
where 
is the fish population after 
years and 
and 
are positive constants that depend on the species and its environment.
is the fish population after years and and are positive constants that depend on the species and its environment.Step-by-step explanation
Step 1.
Let's assume what we want to prove, meaning :
Now if we prove that the above expression is true for 
it means it is always true :
it means it is always true :
We cannot go any further using the inequality so we need to transform the sequence in a way
That allows us to use what we found from the inequality :
However we just found that the term 
will be greater than 
meaning :
will be greater than meaning :
Finally since 
is population it can't be negative:
is population it can't be negative:
We finished proving that 
, Now to prove is decreasing: Let's take again:
, Now to prove is decreasing: Let's take again:
Again we can use the fact that the term 
will be greater than meaning :
will be greater than meaning :
Therefore is increasing.
is increasing.
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1a
- Problem 1b
- Problem 1c
- Problem 2a
- Problem 2b
- Problem 3
- Problem 4
- Problem 5
- Problem 6
- Problem 7
- Problem 8
- Problem 9
- Problem 10
- Problem 11
- Problem 12
- Problem 13
- Problem 14
- Problem 15
- Problem 16
- Problem 17
- Problem 18
- Problem 19
- Problem 20
- Problem 21
- Problem 22
- Problem 23
- Problem 24
- Problem 25
- Problem 26
- Problem 27
- Problem 28
- Problem 29
- Problem 31
- Problem 32
- Problem 33
- Problem 34
- Problem 35
- Problem 36
- Problem 37
- Problem 38
- Problem 39
- Problem 40
- Problem 41a
- Problem 41b
- Problem 42a
- Problem 42b
- Problem 43a
- Problem 43b
- Problem 44
- Problem 45a
- Problem 45b
- Problem 46a
- Problem 46b
- Problem 46c
- Problem 47a
- Problem 47b
- Problem 48
- Problem 49
- Problem 49a
- Problem 50
- Problem 51
- Problem 52
- Problem 53
- Problem 54
- Problem 54
- Problem 54a
- Problem 54b
- Problem 55
- Problem 56
- Problem 57
- Problem 58a
- Problem 58b
- Problem 59a
- Problem 59b
- Problem 59c
- Problem 59d
- Problem 60