As you know, when a course ends, students start to forget the material they have learned.
Homework4: Problem 13
As you know, when a course ends, students start to forget the material they have learned. One model (called the Ebbinghaus model) assumes that the rate at which a student forgets material is proportional to the difference between the material currently remembered and some positive constant, α.
A. Let y = f(t) be the fraction of the original material remembered t weeks after the course has ended. Set up a differential equation tor y. using k as any constant of proportionality you may need (let k>0). Your equation will contain two constants, the constant a (also positive) is less than y for all t.
What is the initial condition for your equation?
B. Solve the differential equation.
C. What are the practical meaning (in terms of the amount remembered) of the constants in the solution y = f(t)? If after one week the student remembers 84 percent of the material learned in the semester, and after two weeks remembers 74 percent, how much will she or he remember after summer vacation (about 14 weeks)?
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As you know, when a course ends, students start to forget the material they have learned.
Results for this submission Entered Answer Preview Result -k (y-a) -k(y - a) correct correct -kt ...
Results for this submission Entered Answer Preview Result -k (y-a) -k(y - a) correct correct -kt a +(1-a) e correct 65 65 incorrect At least one of the answers above is NOT correct (1 point) As you know, when a course ends, students start to forget the material they have learned. One model (called the Ebbinghaus model) assumes that the rate at which a student forgets material is proportional to the difterence between the material currently remembered and some positive...
Question 1: Question 2: 1 point A liquid at temperature F is placed in an oven at temperature oven. Write a differential equation for the temperature Tit) of the liquid. 0 The temperature of the liq...
Question 1:
Question 2:
1 point A liquid at temperature F is placed in an oven at temperature oven. Write a differential equation for the temperature Tit) of the liquid. 0 The temperature of the liquid increases at a rate times the difference between the temperature of the liquid and that of the T(0) Note: use TT', etc instead of T(t), T'(t) in your answers. After you set up your differential equation you will have to set it equal to...
please solve both. thank you! A mass of 1.25 kg stretches a spring 0.06 m. The...
please solve both. thank
you!
A mass of 1.25 kg stretches a spring 0.06 m. The mass is in a medium that exerts a viscous resistance of 56 N when the mass has a velocity of 2 . The viscous resistance is proportional to the speed of the object. Suppose the object is displaced an additional 0.03 m and released. Find an function to express the object's displacement from the spring's equilibrium position, in m after t seconds. Let positive...
Use the solution you found in Part 1f to show that the Gompertz model can be...
Use the solution you found in
Part 1f to show that the Gompertz model can be rewritten as
dP/dt=−λe^(−rt)P, where λ is a positive constant.
j) Consider grouping the factors in the equation like this:
dP/dt=-(λe^(-rt))P. Make an interpretation of this equation. In
other words, what assumption about tumour growth would lead us to
write down such an equation?
k) Now consider grouping the factors in the equation like this:
dP/dt=−λ(e^(-rt)P). Again, explain what assumption about tumour
growth would lead...
Exercises 1. Verify equation (3) 2. Use the techniques of Section 13.7 and the fact that...
Exercises 1. Verify equation (3) 2. Use the techniques of Section 13.7 and the fact that P(0) = 10 to solve equation (5). 3. The carrying capacity of Atlantic harp seals has been estimated to be C = 10 million seals. Let 1 = 0 correspond to the year 1980 when this seal population was estimated to be about 2 mil- lion. (Data from: Fisheries and Oceans Canada.) (a) Use a logistic growth model = kP(C - P) with k...
Part A - SIR model for the spread of disease Overview. This part of the assignment...
Part A - SIR model for the spread of disease Overview. This part of the assignment uses a mix of theory and data to estimate the contact number c=b/k of an epidemic and hence to estimate the infection-spreading parameter b. The point is that once you know the value of b for a certain disease and population, you can use it in your model the next time there is an cpidemic, thus cnabling you to make predictions about the demand...
please answer all prelab questions, 1-4. This is the prelab manual, just in case you need...
please answer all prelab questions, 1-4.
This is the prelab manual, just in case you need background
information to answer the questions. The prelab questions are in
the 3rd photo.
this where we put in the answers, just to give you an
idea.
Lab Manual Lab 9: Simple Harmonic Oscillation Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and...
Experiment 7 - The Resistor Capacitor Circuit Learning Objectives: Understand the short and long time behavior...
Experiment 7 - The Resistor Capacitor Circuit Learning Objectives: Understand the short and long time behavior of circuits containing capacitors. Understand the and the mathematical relationshin between the current through the circuit as a function time, resistance, capacitance, and potential difference 1. Understanding the models for the behavior of a capacitor in a circuit A capacitor is a device that stores energy in a circuit as potential energy in an electric field. In the simple circuit drawn on the night,...
Vibrational Motion Introduction If an object is following Hooke’s Law, then Fnet = -kx = ma...
Vibrational Motion Introduction If an object is following Hooke’s Law, then Fnet = -kx = ma Since acceleration is the second derivative of position with respect to time, the relationship can be written as the differential equation: kx = m δ2xδt2/{"version":"1.1","math":"<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mi>x</mi><mo> </mo><mo>=</mo><mo> </mo><mi>m</mi><mo> </mo><mfrac bevelled="true"><mrow><msup><mi>δ</mi><mn>2</mn></msup><mi>x</mi></mrow><mrow><mi>δ</mi><msup><mi>t</mi><mn>2</mn></msup></mrow></mfrac></math>"} Methods for solving differential equations are beyond the scope of this course; in fact, a class in differential equations is usually a requirement for a degree in engineering or physics. However, the solution to this particular differential...
Can someone help me finish my table? all the inforamtion is there. molarity of HCL =0.5M g...
can someone help me finish my
table? all the inforamtion is there.
molarity of HCL =0.5M
grams of borax = 18.41g
the Relationship between Thermodynamics and Equilibrium 21 Complete the data table for each temperature studied. Beaker Label 42 °C 45 °C 36 ° C 39 °C 33 °C 2EC 138℃-2°C| ーでー 46℃ Temperature reading (C) Absolute temperature (K) 1/T Final buret reading Initial buret reading Volume of HCI Moles of H+ Moles of B Os(OH)2 Molarity of B,Os(OH)2 306.230.2...
Results for this submission Entered Answer Preview Result -k (y-a) -k(y - a) correct correct -kt a +(1-a) e correct 65 65 incorrect At least one of the answers above is NOT correct (1 point) As you know, when a course ends, students start to forget the material they have learned. One model (called the Ebbinghaus model) assumes that the rate at which a student forgets material is proportional to the difterence between the material currently remembered and some positive...
Question 1:
Question 2:
1 point A liquid at temperature F is placed in an oven at temperature oven. Write a differential equation for the temperature Tit) of the liquid. 0 The temperature of the liquid increases at a rate times the difference between the temperature of the liquid and that of the T(0) Note: use TT', etc instead of T(t), T'(t) in your answers. After you set up your differential equation you will have to set it equal to...
please solve both. thank
you!
A mass of 1.25 kg stretches a spring 0.06 m. The mass is in a medium that exerts a viscous resistance of 56 N when the mass has a velocity of 2 . The viscous resistance is proportional to the speed of the object. Suppose the object is displaced an additional 0.03 m and released. Find an function to express the object's displacement from the spring's equilibrium position, in m after t seconds. Let positive...
Use the solution you found in
Part 1f to show that the Gompertz model can be rewritten as
dP/dt=−λe^(−rt)P, where λ is a positive constant.
j) Consider grouping the factors in the equation like this:
dP/dt=-(λe^(-rt))P. Make an interpretation of this equation. In
other words, what assumption about tumour growth would lead us to
write down such an equation?
k) Now consider grouping the factors in the equation like this:
dP/dt=−λ(e^(-rt)P). Again, explain what assumption about tumour
growth would lead...
Exercises 1. Verify equation (3) 2. Use the techniques of Section 13.7 and the fact that P(0) = 10 to solve equation (5). 3. The carrying capacity of Atlantic harp seals has been estimated to be C = 10 million seals. Let 1 = 0 correspond to the year 1980 when this seal population was estimated to be about 2 mil- lion. (Data from: Fisheries and Oceans Canada.) (a) Use a logistic growth model = kP(C - P) with k...
Part A - SIR model for the spread of disease Overview. This part of the assignment uses a mix of theory and data to estimate the contact number c=b/k of an epidemic and hence to estimate the infection-spreading parameter b. The point is that once you know the value of b for a certain disease and population, you can use it in your model the next time there is an cpidemic, thus cnabling you to make predictions about the demand...
please answer all prelab questions, 1-4.
This is the prelab manual, just in case you need background
information to answer the questions. The prelab questions are in
the 3rd photo.
this where we put in the answers, just to give you an
idea.
Lab Manual Lab 9: Simple Harmonic Oscillation Before the lab, read the theory in Sections 1-3 and answer questions on Pre-lab Submit your Pre-lab at the beginning of the lab. During the lab, read Section 4 and...
Experiment 7 - The Resistor Capacitor Circuit Learning Objectives: Understand the short and long time behavior of circuits containing capacitors. Understand the and the mathematical relationshin between the current through the circuit as a function time, resistance, capacitance, and potential difference 1. Understanding the models for the behavior of a capacitor in a circuit A capacitor is a device that stores energy in a circuit as potential energy in an electric field. In the simple circuit drawn on the night,...
can someone help me finish my
table? all the inforamtion is there.
molarity of HCL =0.5M
grams of borax = 18.41g
the Relationship between Thermodynamics and Equilibrium 21 Complete the data table for each temperature studied. Beaker Label 42 °C 45 °C 36 ° C 39 °C 33 °C 2EC 138℃-2°C| ーでー 46℃ Temperature reading (C) Absolute temperature (K) 1/T Final buret reading Initial buret reading Volume of HCI Moles of H+ Moles of B Os(OH)2 Molarity of B,Os(OH)2 306.230.2...
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