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Problem

Suppose that a population develops according to t…

05:20

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Problem 2 Easy Difficulty

A population grows according to the given logistic equation, where $ t $ is measured in weeks.
(a) What is the carrying capacity? What is the value of $ k? $
(b) Write the solution of the equation.
(c) What is the population after 10 weeks?
$ \frac {dP}{dt} = 0.02P - 0.0004P^2, P(0) = 40 $


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Related Courses

Calculus 2 / BC

Calculus: Early Transcendentals

Chapter 9

Differential Equations

Section 4

Models for Population Growth

Related Topics

Differential Equations

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Differential Equations - Overview

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

Video Thumbnail

33:32

Differential Equations - Example 1

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

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Watch More Solved Questions in Chapter 9

Problem 1
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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

Video Transcript

hey is clear. So when you right here. So we're given the DP over. DT was equal to zero point zero to pee minus zero point 00 Thorough for peace where we got factor out A 0.2 p, you know, one minus 0.2 and this is equal to 0.2 p times one minus p over 50 for part B. We know that the carrying capacity is gonna be part is gonna be 50 part, eh? And we know K is equal to point 02 So we know that M is equal to 50 and p of zero is equal to 40. So for our A value, which is equal to 50 minus 40 over 40 which is equal to point 25 So our solution is P of tea is equal to 50 over one plus 0.25 eats the negative 0.2 tea for part C. We have the equation from part B. So we're looking at the population 10 weeks after, so we just plug in p of tea and this is around 41

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Top Calculus 2 / BC Educators
Catherine Ross

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Lectures

Video Thumbnail

13:37

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A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

Video Thumbnail

33:32

Differential Equations - Example 1

A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.

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