Chapter 6.3, Problem 60E

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347

Chapter
Section

### Calculus (MindTap Course List)

11th Edition
Ron Larson + 1 other
ISBN: 9781337275347
Textbook Problem

# Solving a Logistic Differential Equation In Exercises 57-60, find the logistic equation that passes through the given point. d y d t = 3 y 20 − y 2 1600 ,     ( 0 , 15 )

To determine

To calculate: The logistic equation that satisfies the initial condition (0,15) and the value of y at theconditions t=5 and t=100 where dydt=3y20y21600

Explanation

Given:

The differential logistic equation is dydt=3y20âˆ’y21600. The initial condition is (0,15) and the given condition is t=5Â andÂ t=100.

Formula used:

The general logistic equation is y=L1+beâˆ’kt.

Calculation:

Consider the expression dydt=3y20âˆ’y21600:

dydt=3y20âˆ’y21600dydt=3y20(1âˆ’y240)

Here k=320Â andÂ L=240.

Put these values in y=L1+beâˆ’kt:

y=L1+beâˆ’kty=2401+beâˆ’320t

The initial condition is t=0Â andÂ y=8

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