A student is attempting to find an equation for a line that passes through two points. Which statement best applies to the mathe
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Here we want to solve differential equations, we will see that the general solution is:
We want to solve the differential equation:
From this is pretty clear that y is an exponential function, with an exponent of -1*t.
We can write it generally as:
Then if we set B = 100 we get:
So we just found the general form of the function.
Now we have two cases:
A) y(0) = 35
In this case, the function is:
B) y(0) = 125
In this case, the function is:
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 <em>person can learn</em> (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 <u>D: none of the above.</u>
If you want to learn more, you can read:
Cost of each juice boxes is $ 0.68 and cost of each water bottle is $ 0.24
<em><u>Solution:</u></em>
Let "j" be the cost of each juice box
Let "w" be the cost of each bottles of water
<em><u>One teacher purchased 18 juice boxes and 32 bottles of water and spent $19.92</u></em>
Therefore, we frame a equation as:
18 x cost of each juice box + 32 x cost of each bottles of water = 19.92
18j + 32w = 19.92 ------ eqn 1
<em><u>The other teacher Purchased 14 Juice Boxes and 26 Boxes of water and spent $15.76</u></em>
Therefore, we frame a equation as:
14 x cost of each juice box + 26 x cost of each bottles of water = 15.76
14j + 26w = 15.76 ----------- eqn 2
<em><u>Let us solve eqn 1 and eqn 2</u></em>
<em><u>Multiply eqn 1 by 7</u></em>
126j + 224w = 139.44 -------- eqn 3
<em><u>Multiply eqn 2 by 9</u></em>
126j + 234w = 141.84 ---------- eqn 4
<em><u>Subtract eqn 3 from eqn 4</u></em>
126j + 234w = 141.84
126j + 224w = 139.44
( - ) --------------------
10w = 2.4
Divide both sides by 10
w = 0.24
<em><u>Substitute w = 0.24 in eqn 1</u></em>
18j + 32(0.24) = 19.92
18j + 7.68 = 19.92
18j = 12.24
Divide both sides by 18
j = 0.68
Thus cost of each juice boxes is $ 0.68 and cost of each water bottle is $ 0.24