SOLUTION: An experiment consists of mixing 2 liquids and observing the change in temperature of the mixture. The results are presented in the table below. time elapsed temp

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Question 103189: An experiment consists of mixing 2 liquids and observing the change in temperature of the mixture. The results are presented in the table below.
time elapsed temperature
(in min.) (in °C)
2 26.9
4 31.5
7 38.4
10 45.3
The phenomenon can be expressed by a linear functionwhich associates the temperature f(T) of the mixture with the elapsed time t.
What equation represents this function?
Answer by HyperBrain(694) About Me  (Show Source):
You can put this solution on YOUR website!
Assuming that this represents a STRAIGHT LINE, any two pairs will do.
slope=%28y-increment%29%2F%28x-increment%29
I will use these pairs---(2,26.9), and (4,31.5)

Thus,
slope=%2831.5-26.9%29%2F%284-2%29
slope=4.6%2F2
slope=2.3

Let's use the slope intercept form!

y=mx%2Bb

Since we DO NOT know the y-intercept,b, we'll solve for it!
Let's use the pair,(4,31.5) for the values of x and y.
31.5=2.3%2A4%2Bb
31.5=9.2%2Bb
b=22.3
Thus,
y=2.3x+22.3
This can be written as a function
f(t)=2.3T+22.3

read as,'the f of the time is 2.3 times the temp. added to 22.3.
GRAPH:
graph%281000%2C1000%2C-50%2C50%2C-50%2C50%2C2.3x%2B22.3%29

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HyperBrain!