Let P(t) be the number of fruit flies in a jar t days later. Experimentally, we know dP =0.1P dt " -air (1-) t 2 0. 400 we assume that P(t) 20 for all t 0. Let P(0) = a. nen a > 0 and a + 400, find P(t) for allt 0. Write the solution in terms of a.
Let P(t) be the number of fruit flies in a jar t days later. Experimentally, we know dP =0.1P dt " -air (1-) t 2 0. 400 we assume that P(t) 20 for all t 0. Let P(0) = a. nen a > 0 and a + 400, find P(t) for allt 0. Write the solution in terms of a.
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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b) find the equilibrium solution to the given differential equation.
C) what happens to P(t), if a =0 or a =400? Explain
D) Determine whether the equilibrium solution in b are stable or not. Explain the reasons for your answer. Using the result of (a) may be helpful
I need help on question C and D
![Let \( P(t) \) be the number of fruit flies in a jar \( t \) days later. Experimentally, we know
\[
\frac{dP}{dt} = 0.1P \left( 1 - \frac{P}{400} \right), \quad t \geq 0.
\]
We assume that \( P(t) \geq 0 \) for all \( t \geq 0 \). Let \( P(0) = a \).
When \( a > 0 \) and \( a \neq 400 \), find \( P(t) \) for all \( t \geq 0 \). Write the solution in terms of \( a \).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6cbadd76-3844-416d-aad4-7be877c4787a%2Fa0919c92-7ea1-4e8c-93ca-ea9a05a9ffc9%2F1v925u_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let \( P(t) \) be the number of fruit flies in a jar \( t \) days later. Experimentally, we know
\[
\frac{dP}{dt} = 0.1P \left( 1 - \frac{P}{400} \right), \quad t \geq 0.
\]
We assume that \( P(t) \geq 0 \) for all \( t \geq 0 \). Let \( P(0) = a \).
When \( a > 0 \) and \( a \neq 400 \), find \( P(t) \) for all \( t \geq 0 \). Write the solution in terms of \( a \).
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