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
In the accompanying figure, triangle ABC has coordinates A(0,3), B(7,3), C(7,7). What is the area of triangle ABC in square unit
ElenaW [278]

We know area of triangle = \frac{1}{2}  * base * height

In triangle ABC , AB is the base and BC is the height

Now we find the distance between A and B

Distance formula is \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}

A(0,3), B(7,3)

Distance AB = \sqrt{(7-0)^2 + (3-3)^2}

= \sqrt{(7)^2 } = 7

B(7,3), C(7,7)

Distance BC = \sqrt{(7-7)^2 + (7-3)^2}

= \sqrt{(4)^2 } = 4

area of triangle = \frac{1}{2}  * base * height

area of triangle = \frac{1}{2}  * AB * BC

= \frac{1}{2}  * 7 * 4 = 14 units ^2

4 0
3 years ago
Last One Please Help
tigry1 [53]

Answer: A. 3/5

Step-by-step explanation:

Count all the add numbers in 1-10 then add the 4 and you get

6/10

Simply and you get 3/5

7 0
3 years ago
Suppose a normal distribution has a mean of 266 and a standard deviation of
Elis [28]

Answer:

I think the answer is P(x>178)

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
What is the mode of the following numbers?<br> 3,7, 5, 2, 5, 5, 2,5
tangare [24]

The mode is 5.ㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤㅤ

8 0
2 years ago
Read 2 more answers
If f(x) = 6x − 5 and f(5a) = 73, then what is the value of a?
Dmitrij [34]

Answer:

a =13/5

Step-by-step explanation:

f(x) = 6x − 5

f(5a) = 6*5a − 5=73

       30a -5 = 73

Add 5 to each side

    30a -5+5 = 73+5

      30a =78

Divide  by 30

30a/30 = 78/30

a =13/5

4 0
2 years ago
Read 2 more answers
Other questions:
  • Andy’s total bill for lunch was$20. The cost of the drink was 15 percent of the total of the bill and the rest is the cost of th
    15·1 answer
  • What’s is 2000+100.000
    13·2 answers
  • A hot air balloon descends 15 feet each minute after having reached an altitude of 362 feet above the ground. What is the altitu
    6·1 answer
  • A bank records deposits as positive numbers and withdrawals as negative numbers. Mike withdrew $60\$60 $60 dollar sign, 60 from
    9·1 answer
  • G=r-d+ca solve for a
    9·1 answer
  • What is the longest flagpole ( in whole feet) that could be shipped in a box that measures 2ft by 2 ft by 12 ft
    13·1 answer
  • Very easy! 15 points!
    5·1 answer
  • F(2)=7 into coordinate points
    5·1 answer
  • The speed limit on 1-35 is 80 miles per hour. How far can Mrs.Mindy drive in 2 1/2 hours?
    12·1 answer
  • Someone help me with this for BRAINLIEST thank you!
    11·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!