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. 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). (Assume the constant of proportionality is k > 0. Use A for A(t)

And the solution for this equation is:

Using the substitution u = M-A, we have that du = -dA and after integrate we got:

C is a constant.

Now we can apply exponential in both sides and we got:

Step-by-step explanation:

Let's define some notation first :

represent the total amount of the subject to be memorized

represent the amount memorized at time t

t represent the time

k is a constant of proportionality

For this case we know that the rate of memorizing is proportional to the amount left to be memorized.

So then we can create the following relationship:

Where k>0. We can solve this differential equation like this:

Using the substitution u = M-A, we have that du = -dA and after integrate we got:

C is a constant.

Now we can apply exponential in both sides and we got:

spinning a 1, 2, or 3. option d.

step-by-step explanation: when spinning a number graph up to 4, and aiming for any number less than 3, that automatically eliminates the number 4. now you have two numbers to spin on that are less than 3, but the number 3 is included in this question because it's no greater of an number than itself. i hope this you : )