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

See similar textbooks

Related questions

Q: Find the equilibria of the differential equation, and construct the phase plot: y' (y − 3)(y – 5).…

Q: A population of insects grows at a rate that is given by dN = 0.078N dt - If there are initially 100…

Q: A student is solving a separable differential equation and gets this far: ly=(x²3)dx What is the…

A: Integration is used to determine the bigger value by adding all the small parts. While…

Q: Newton's Law of Cooling.) Let T(t) be the temperature of an object in a room of fixed ambient…

Q: You prescribe an antibiotic to a patient to cure an infection. We know that the rate of change of…

Q: dy = 1 – x – 2y and y = 3 when x dx 1. %3D 8. Approximate y(0.7) if %3D Use h = -0.l as the step…

A: Given: dydx=1-x-2y y1=3 step size h=-0.1 Euler’s method yields:…

Q: A medication is administered to a patient. The amount, in milligrams, of the medication in the…

A: We have given an autonomous differential equation dydt=12-y3 We sketch the solution curve and find…

Q: the rate of change in the value of bills investment in bitcoin obeys the differential equation…

A: We have to find bill invest initially in bitcoin 6 years ago , the rate of change in bill's…

Q: Given the following logistic differential which models population growth. equation Identify the…

Q: Concentration of Carbon Monoxide (CO) in the Air According to a joint study conducted by Oxnard's…

A: The concentration of CO in the air due to automobile exhaust t year from now is given by the…

Q: Consider a pond that initially contains 10 million gal of fresh water. Water containing an…

Q: a) How is ds/dt related to dx/dt if y is constant? ds/dt=___(dx/dt)

A: Consider a function S with variable x and y as constant. S=fx+ywhere, fx=function with x as…

Q: A particle moves along the x-axis with its position at time t given by s (t) = t – 5t, t> 0.…

Q: (c) y" – y' = t², y(0) = y'(0) = 0.

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.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Differential Equation$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.

Similar questions

A = k· A 1. The radioactive isotope lead, Pb-209, decays at a rate proportional to the amount present at time t and has a half-life of 3.3 hours. If 1.5 grams of this isotope is present initially, answer the following: a) Find the complete model. A(t) = A₁ekt b) How long will it take for 30% of the lead to decay? (Round to the tenths place.) c) How much lead is present after 5 hours? (Round to the hundredths place.) d) At what rate is the lead decaying after 5 hours? (Round to the hundredths place.)
Consider the model of Newton's law of cooling and warming given by: IP dt 40 -T T(0) = To- %3D 4 The differential equation describes the model in which the object in the model increases as time goes by. Select one: O True O False
Please give me Hundred Percent correct answer in the order to get positive feedback please show me neat and clean work
Find and classify the equilibria for y' = (y - 1)(y - 2)y. %3D The initial
Solve re"y = e +a'e2. %3D y(z) =D (Use C to denote an arbitrary constant.)
Consider the IVP: x" + (x')² + 6tx = 0, x(0) = 3, x'(0) = 4 %3D Using the Euler method with a time step of At = 0.4 approximate x(0.8) to the nearest thousandth (3 decimal places).
dy (i) Solve (X²D² + 4xD + 2)y = logx, given that x = 1, y = 0 and = 0. %3D dx
Population of the world, (x) is assumed to be a continuous variable at time t years. The rate of increase of x due to birth is ax and the rate of decrease of x due to death is Bx, where a and B are positive constant. a. By applying differential equation concept and assuming a = 0.060 and B = 0.040. Show the population of the world (x) double itself in approximately 35 years. Justify your answer. b. By using appropriate scale, draw the graph of world population growth.
Consider the differential equation equation: y" () + y(x) = xe" where y(0) = 0 and y(pi/2) = 2. Determine the value of y(x) at x - 0.25. %3! Your Answer: Answer
%3D %3D Solve the IVP y"+ 4y/ + 5y = 38,(t), y(0) = 0, y'(0) = 1.
Identify equilibrium values and determine which are stable and which are unstable.dy/dx = (y+4)(y+3)A. y=4 is stable, y=3 unstableB. y=-3 is stable, y=4 unstableC. y=-4 is stable, y=3 is unstableD. y=3 is stable, y=-4 is unstable
Laboratory department detects the concentration C of impurity of an oil purifier changes with time t and is described by the equation = b+ dm - Cm, where b,d,a and m are dt constants. Given C = Co and when t = 0. Solve the equation and show that -mt -mt c = + a][1- e=]+ coe