Ms Soltau is brewing a vat of squareroot beer on the stove S

Ms. Soltau is brewing a vat of squareroot beer on the stove. She needs to cool it to 70 degree F to be able to run. through the plastic tubing to bottle it. The liquid was boiling (212 degree F) when she removed it from the stove and put it outside in a snow bank. The outside temperature was 20 degree F. After 20 minutes s e measured the temperature, and found that it was 165 degree F. She used this to determine the equation for the cooling of the liquid: (x) = 192 0.986^(x). What type of equation is this? What does x represent? What does y represent? What is the initial value of this equation? Why do you think it isn\'t 212 degree F? Since the difference between her goal temp, and the outside temp is 50 degree F, determine how long it will take for the liquid to cool enough for her to bottle it.

Solution

a. This is an exponential equation. Here, x represents the time in minutes and y represents the temperature of the liquid.

b. The inital value is 192^o F.

When we put x=0, we get y = 192^oF.

c. Since the out side temperatue is 20^o F. Thus the temperatue of the liquid will be 70^o F.

Now 70 = 192.0.986^x₁

or 70/192 = .0.986^x₁

taking log of both side, we get

log(70/192) = x₁ log(.0.986)

Thus       x₁ = 71.56 minute

And for 20F

log(20/192) = x₂ log(.0.986)

x₂ = 160.40.

The difference in the time = 88.86 minutes

  Therefore it takes 88.86 minutes . Ans