Part 2: Free Response 1. During a chemical reaction, the function y = f (t) models the amount of a substance present, in grams, at time t seconds. At the start of the reaction (t = 0), there are 10 grams of the substance present. The function dy y = f (t) satisfies the differential equation -0.02y². dt %3D (a) Use the line tangent to the graph of y = f (t) at t = 0 to approximate the amount of the substance remaining at time t = 2 seconds. (b) Using the given differential equation, determine whether the graph of f could resemble the following graph. Give a reason for your answer. y dy –0.02y² with the initial dt (c) Find an expression for y = f (t) by solving the differential equation condition f (0) = 10.
Part 2: Free Response 1. During a chemical reaction, the function y = f (t) models the amount of a substance present, in grams, at time t seconds. At the start of the reaction (t = 0), there are 10 grams of the substance present. The function dy y = f (t) satisfies the differential equation -0.02y². dt %3D (a) Use the line tangent to the graph of y = f (t) at t = 0 to approximate the amount of the substance remaining at time t = 2 seconds. (b) Using the given differential equation, determine whether the graph of f could resemble the following graph. Give a reason for your answer. y dy –0.02y² with the initial dt (c) Find an expression for y = f (t) by solving the differential equation condition f (0) = 10.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
![Part 2: Free Response
1.
During a chemical reaction, the function y = f (t) models the amount of a substance present, in grams, at
time t seconds. At the start of the reaction (t = 0), there are 10 grams of the substance present. The function
dy
y = f(t) satisfies the differential equation
:-0.02y?.
dt
(a) Use the line tangent to the graph of y = f (t) at t = 0 to approximate the amount of the substance
remaining at time t = 2 seconds.
(b) Using the given differential equation, determine whether the graph of f could resemble the following
graph. Give a reason for your answer.
y
(c) Find an expression for y = f (t) by solving the differential equation
dy
-0.02y? with the initial
dt
condition f (0) = 10.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5498129d-fa90-4054-9767-1cffe54599e5%2F01674052-49c7-4c7e-9256-9dc0dfacf81b%2F8p0jzrj_processed.png&w=3840&q=75)
Transcribed Image Text:Part 2: Free Response
1.
During a chemical reaction, the function y = f (t) models the amount of a substance present, in grams, at
time t seconds. At the start of the reaction (t = 0), there are 10 grams of the substance present. The function
dy
y = f(t) satisfies the differential equation
:-0.02y?.
dt
(a) Use the line tangent to the graph of y = f (t) at t = 0 to approximate the amount of the substance
remaining at time t = 2 seconds.
(b) Using the given differential equation, determine whether the graph of f could resemble the following
graph. Give a reason for your answer.
y
(c) Find an expression for y = f (t) by solving the differential equation
dy
-0.02y? with the initial
dt
condition f (0) = 10.
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