1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Lelechka [254]
3 years ago
14

In the theory of learning, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to

be memorized. Assume that the rate at which material is forgotten is proportional to the amount memorized. Suppose M denotes the total amount of a subject to be memorized and A(t) is the amount memorized in time t > 0. Determine a differential equation for the amount A(t) when forgetfulness is taken into account. (Assume the constants of proportionality for the rate at which material is memorized and the rate at which material is forgotten are k1 > 0 and k2 > 0, respectively. Use A for A(t).)
dA/dt =
Mathematics
1 answer:
babymother [125]3 years ago
7 0

Answer:

dA/dt = k1(M-A) - k2(A)

Step-by-step explanation:

If M denote the total amount of the subject and A is the amount memorized, the amount that is left to be memorized is (M-A)

Then, we can write the sentence "the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized" as:

Rate Memorized = k1(M-A)

Where k1 is the constant of proportionality for the rate at which material is memorized.

At the same way, we can write the sentence: "the rate at which material is forgotten is proportional to the amount memorized" as:

Rate forgotten = k2(A)

Where k2 is the constant of proportionality for the rate at which material is forgotten.

Finally, the differential equation for the amount A(t) is equal to:

dA/dt = Rate Memorized - Rate Forgotten

dA/dt = k1(M-A)  - k2(A)

You might be interested in
How do i solve 3y = 15x -2
Simora [160]

Answer:

2

Step-by-step explanation:

3 0
2 years ago
Read 2 more answers
It is given that 2(3+x)=6+2x. this is an example of the ____ property.
hoa [83]
I believe this is the distributive property.
6 0
3 years ago
Read 2 more answers
a language arts test is worth 100 points there is a total of 26 questions . there are spelling word questions that ae worth 2 po
natka813 [3]

10 question of spelling words and 16 questions of vocabulary are present

<em><u>Solution:</u></em>

Let "x" be the number of spelling word questions

Let "y" be the number of vocabulary word question

<em><u>There is a total of 26 questions. Therefore, we get</u></em>

number of spelling word questions + number of vocabulary word question = 26

x + y = 26 --------- eqn 1

<em><u>There are spelling word questions that worth 2 points each and vocabulary word question worth 5 points each</u></em>

The language arts test is worth 100 points

Therefore, we frame a equation as:

number of spelling word questions x 2 + number of vocabulary word question x 5 = 100

x \times 2 + y \times 5 = 100

2x + 5y = 100 --------- eqn 2

<em><u>Let us solve eqn 1 and eqn 2</u></em>

From eqn 1,

x = 26 - y ------- eqn 3

<em><u>Substitute eqn 3 in eqn 2</u></em>

2(26 - y) + 5y = 100

52 - 2y + 5y = 100

3y = 100 - 52

3y = 48

<h3>y = 16</h3>

<em><u>Substitute y = 16 in eqn 3</u></em>

x = 26 - 16

<h3>x = 10</h3>

Thus 10 question of spelling words and 16 questions of vocabulary are present

4 0
3 years ago
If you pour 3 gallons of paint into 8 cans how much will be in each can​
bezimeni [28]

Answer:

pours 3 gallons of paint equally into 5 cans. How many gallons of paint will there be in each can? ... Did you divide to get the answer? ... If two gallons of paint is needed to paint a 40 sq meter wall, how many gallons of paint ... Hamza bought 8 gallons of brown paint to paint his kitchen and dining room

4 0
2 years ago
Read 2 more answers
How to write 5(2x+1)(x+1) in standard form explain....?
earnstyle [38]

1.So the problem "y=2x+5" is in standard form and no modification is necessary. For a parabolic equation, the standard form is y = a(x - h)^2 + k, from which direction (polarity of "a") and axis of symmetry (value of "h"), etc.

2.Ax + By + C = 0 or Ax + By = C.

6 0
3 years ago
Read 2 more answers
Other questions:
  • As an estimation we are told £3 is €4.<br> Convert €20 to pounds.
    9·1 answer
  • Karen began her tennis game at 9:30. She played for two and a half hours.What time did she finish?
    14·1 answer
  • A researcher would like to determine whether a new tax on legalized marijuana has had any effect on people’s purchasing behavior
    15·1 answer
  • Geometry, I will give brainliest. I need help fast
    11·1 answer
  • Y=x^2-6x+3 help write the vertex form of the equation
    6·1 answer
  • Find the value of x,given the area of the quadrilateral
    10·1 answer
  • 10. On the playground, Grace threw the ball 3 more feet than Ella. Grace threw the ball 21
    15·1 answer
  • Sanjay and his friends are doing a physics lab on air pressure. First, they fill a balloon with air until it reaches a pressure
    13·1 answer
  • In the number 725.78, how does the value of the 7 in the tenths place compare to the value of the 7 in the hundreds place?
    6·2 answers
  • ℎ ℎ 22 2 22 2− 3 +10
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!