So from a table, we want to find an equation that models the mass as a function of time, we will get the equation:
M(t) = 0.02*t^2 - 2.42*t + 99.57
And with that equation, we will find that the mass after 11 seconds is 75 grams.
From the table we have the points:
(2, 94.8)
(5, 87.9)
(8, 81.3)
And we know that this follows a quadratic model, then we have:
M(t) = a*t^2 + b*t + c
Notice that from the known points, we have 3 equations:
94.8 = a*2^2 + b*2 + c
87.9 = a*5^2 + b*5 + c
81.3 = a*8^2 + b*8 + c
So we have a system of equations, we can simplify the equations to get:
94.8 = a*4 + b*2 + c
87.9 = a*25 + b*5 + c
81.3 = a*64 + b*8 + c
To solve this, we start by isolating one of the variables in one of the equations, let's isolate c in the first one.
c = 94.8 - a*4 - b*2
now we replace this in the other two equations to get:
87.9 = a*25 + b*5 + (94.8 - a*4 - b*2)
81.3 = a*64 + b*8 + ( 94.8 - a*4 - b*2)
Now we simplify these two equations to get:
-6.9 = a*21 + b*3
-13.5 = a*60 + b*6
Now we do the same thing, I will isolate b in the first equation:
b = (-6.9 - a*21)/3 = -2.3 - a*7
Now we replace this in the other equation:
-13.5 = a*60 + (-2.3 - a*7)*6
Now we can just solve this for a:
-13.5 = a*(60 - 7*6) - 2.3*6
0.3 = a*18
0.3/18 = a = 0.016
Wich can be rounded to:
a = 0.02
Then the value of b is:
b = -2.3 - a*7 = -2.3 - 0.016*7 = -2.42
And the value of c is:
c = 94.8 - a*4 - b*2 = 94.8 - 0.016*4 - (-2.42)*2 = 99.57
So the equation is:
M(t) = 0.02*t^2 - 2.42*t + 99.57
Now we can evaluate this in t = 11s to get:
M(11) = 0.02*11^2 - 2.42*11 + 99.57 = 75.37
Wich can be rounded to 75 grams.
If you want to learn more, you can read:
https://brainly.com/question/20067450
