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The rate of change of a certain population P at time t is modelled by the equation· dt = (100 –P). Initially P = 2000. (a) Determine an expression for P in terms of t. (b) Describe how the population changes over time.

The rate of change of a certain population P at time t is modelled by the equation· dt = (100 –P). Initially P = 2000. (a) Determine an expression for P in terms of t. (b) Describe how the population changes over time.

Calculus: Early Transcendentals
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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Please can you help me with this question? 

when I attempted it I got P = 100 - 1900e-t

After I integrated 1/(100 - P) I got -ln|100 - P| 

Thank you so much.

8 The rate of change of a certain population Pat time t is modelled by the equation = (100– P). dP dt Initially P = 2000. (a) Determine an expression for P in terms of t. (b) Describe how the population changes over time.
Transcribed Image Text:8 The rate of change of a certain population Pat time t is modelled by the equation = (100– P). dP dt Initially P = 2000. (a) Determine an expression for P in terms of t. (b) Describe how the population changes over time.
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