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

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Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

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.

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