Natalie performs a chemistry experiment where she records th

Natalie performs a chemistry experiment where she records the temperature of an ongoing reaction. The solution is 93.5 degrees C after 3 minutes; 90 degrees C after 9 minutes; 70.2 degreesC after 18 minutes; 54.4 degrees C after 30 minutes; 42.5degrees C after 37 minutes; and 24.9degrees C after 48 minutes. Perform a linear regression on this data to complete the following items.

29)Write the equation of the best-fitting line (Round to the nearest Thousandths.)

30) On average how much does the temperature decrease every five minutes?

31)If Natalie\'s solution is expected to freeze at -7 degrees C, how many minutes into the experiment should the solution freeze? (Show work that supports your prediction and round to the nearest minute.)

Solution

a)
P1(3,93.5)
P2(48,24.9)

m=(24.9-93.5)/(48-3)
m=-68.6/45
m=-1.524.

write the equation of the line:

Y-Y1=m(X-X1)
Y-93.5=-1.524(x-3)
Y=-1.524(X-3)+93.5.

b) using the equation:
when X= 5 Y= 90.452
X= 10 Y=82.832
X= 15 Y= 75.212
X= 20 Y= 67.592

Since its a line, the difference between each point is always 7.62. On average the temperature decreases 7.62°C every 5 minutes.

c)
T=-7°C.
those Y=-7.
-7=-1.524(x-3)+93.5.
-7=-1.524(X-3)+93.5.
(-7-93.5)/(-1.524)=X-3
65.94+3=x.
68.94=X.
Rounding up, in 69 minutes the solution will freeze
at T=-7°C.