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Here we want to solve differential equations, we will see that the general solution is:
[tex]y = A*e^{-t} + 100[/tex]
We want to solve the differential equation:
[tex]\frac{dy}{dt} = 100 - y[/tex]
From this is pretty clear that y is an exponential function, with an exponent of -1*t.
We can write it generally as:
[tex]y = A*e^{-t} + B\\\\\frac{dy}{dt} = -A*e^{-t}[/tex]
Then if we set B = 100 we get:
[tex]y = A*e^{-t} + 100\\\\\frac{dy}{dt} = -A*e^{-t} \\\\\frac{dy}{dt} = -A*e^{-t} - 100 + 100 = -y + 100[/tex]
So we just found the general form of the function.
Now we have two cases:
A) y(0) = 35
[tex]y(0) = A*e^{-0} + 100 = 35\\= A + 100 = 35\\\\A = 35 - 100 = -65[/tex]
In this case, the function is:
[tex]y = -65*e^{-t} + 100[/tex]
B) y(0) = 125
[tex]125 = A*e^0 + 100\\\\\125 - 100 = A\\\\25 = A[/tex]
In this case, the function is:
[tex]y = 25*e^{-t} + 100[/tex]
Now we want to see which one of the two can represent how a person learns. Just look at the graph below:
The green line is the one for y(0) = 35, and the blue one is for y(0) = 125.
Notice that for small values of t, the blue function is really large, thus it can't really model how a person learns (is larger for smaller values of t than for larger values).
So y(0) = 35 represents better how a person can learn (but not exactly, because you can see that it eventually becomes almost constant, which is something that really does not happen) so the correct option is D: none of the above.
If you want to learn more, you can read:
https://brainly.com/question/353770
