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?

“Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

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?

College Algebra

7th Edition

ISBN:9781305115545

Author:James Stewart, Lothar Redlin, Saleem Watson

Publisher:James Stewart, Lothar Redlin, Saleem Watson

Chapter2: Functions

Section: Chapter Questions

Problem 30P: In this problem you are asked to find a function that models in real life situation and then use the...

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