Question

The table shows the mass of a substance decreasing over a period of time during a chemical experiment.

Answer 1

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:

brainly.com/question/20067450