3. A population of fish is living in an environment with limited resources. As a consequence,the environment can only support the population if it contains no more than 100,000 fish(otherwise some fish would starve due to an inadequate supply of food, etc.). This particularpopulation of fish (measured in # of fish) as a function of time (measured in years), P(t), isoften modeled by the function100, 000etP(t)et +3(a) What is the initial population of fish?1(b) What is the meaning of P'(t)? What are the units of P'(t)?(c) Find P'(t) and show that it is always positive. What does this suggest about the popu-lation?(d) A different population of fish is modeled by the function Q(t), graphed below.40000y = Q(t)30000200001000012456.Make a rough sketch of the graph of Q'(t). Is Q'(t) always positive?

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3. A population of fish is living in an environment with limited resources. As a consequence, the environment can only support the population if it contains no more than 100,000 fish (otherwise some fish would starve due to an inadequate supply of food, etc.). This particular population of fish (measured in # of fish) as a function of time (measured in years), P(t), is often modeled by the function 100, 000et et + 3 P(t) = (a) What is the initial population of fish? 1 (b) What is the meaning of P'(t)? What are the units of P'(t)? (c) Find P'(t) and show that it is always positive. What does this suggest about the popu- lation?

3. A population of fish is living in an environment with limited resources. As a consequence, the environment can only support the population if it contains no more than 100,000 fish (otherwise some fish would starve due to an inadequate supply of food, etc.). This particular population of fish (measured in # of fish) as a function of time (measured in years), P(t), is often modeled by the function 100, 000et et + 3 P(t) = (a) What is the initial population of fish? 1 (b) What is the meaning of P'(t)? What are the units of P'(t)? (c) Find P'(t) and show that it is always positive. What does this suggest about the popu- lation?

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

3. A population of fish is living in an environment with limited resources. As a consequence,
the environment can only support the population if it contains no more than 100,000 fish
(otherwise some fish would starve due to an inadequate supply of food, etc.). This particular
population of fish (measured in # of fish) as a function of time (measured in years), P(t), is
often modeled by the function
100, 000et
P(t)
et +3
(a) What is the initial population of fish?
1
(b) What is the meaning of P'(t)? What are the units of P'(t)?
(c) Find P'(t) and show that it is always positive. What does this suggest about the popu-
lation?
(d) A different population of fish is modeled by the function Q(t), graphed below.
40000
y = Q(t)
30000
20000
10000
1
2
4
5
6.
Make a rough sketch of the graph of Q'(t). Is Q'(t) always positive?

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