Espresso machine steam heating and coffee cooling problems

[moenste]

In the video, the numbers were chosen to make the percent change exactly 50% for two consecutive data points. For real data, you cannot expect the data to be perfectly exponential, or perfectly linear, etc. You are just trying to discover if the data is "well described" by exponential behavior, or linear behavior, etc.

For the data in the problem, the percent decrease is fairly constant at around 15%. If you had to pick between exponential or linear behavior, which would you choose?

For determining the temperature at t = 12 s, I would not recommend your method.

In that case it indeed can be described by exponential. I though the numbers should be exactly the same, and not somewhat similar like in my case.

Do you have a suggestion how to find the temperature at t = 12 s?

 

[TSny]

Do you have a suggestion how to find the temperature at t = 12 s?

First get the temperature at t = 10 seconds using an assumption of exponential behavior. Then go to t = 12 s.

 

[moenste]

First get the temperature at t = 10 seconds using an assumption of exponential behavior. Then go to t = 12 s.

But what percentage to use?

48 °C / 41 °C = 1.17
41 °C / t_{10 s} = 1.17
t_{10 s} = 35.02 °C

35.02 °C / t_{12 s} = 1.17
t_{12 s} = 29.93 °C

Like that?

 

[TSny]

You could average the four percent changes that you initially calculated. Use that average percent change to fill out the rest of the table.