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1. A curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve?

1. A curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve?

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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1. A curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? 2. The rate of change of bears, N, in a population is directly proportional to 350-N. Time, t, is measured in years. When t=0, the population is 100 and when t = 2, the population has increased to 250. a.) Write and solve a differential equation that describes this situation. b.) Find the bear population in 3 years. c.) Find lim N(t) 1-00
Transcribed Image Text:1. A curve passes through the point (0,5) and has the property that the slope of the curve at every point P is twice the y-coordinate of P. What is the equation of the curve? 2. The rate of change of bears, N, in a population is directly proportional to 350-N. Time, t, is measured in years. When t=0, the population is 100 and when t = 2, the population has increased to 250. a.) Write and solve a differential equation that describes this situation. b.) Find the bear population in 3 years. c.) Find lim N(t) 1-00
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