Temperatures

Question

Temperature were taken after every 10 minutes for 4 experiments.

 

Experiment 1: 52°, 26°, 13°

 

Experiment 2: 28°, 56°, 84°

 

Experiment 3: 14°, 28°, 56°

 

Experiment 4: 67°, 54°, 41°

 

Which of the experiments' temperature have a proportional relationship with time?

 

A. experiment 1

 

B. experiment 2

 

C. experiment 3

 

D. experiment 4

Answer 1

A directly proportional relationship means that the increase in temperature for the first 10 minutes equals the increase in temperature for the second 10 minutes.

We could express that as   (T2 – T1)/10 = (T3 – T2)/10

So, let's calculate the change in temperature:

  Experiment 1:     52 -------- 26 --------13
                                -26/10      -13/10              not equal

  Experiment 2:     28 -------- 56 -------- 84
                                 28/10         28/10             equal

  Experiment 3:     14 -------- 28 -------- 56
                                 14/10          28/10             not equal

  Experiment 4:     67 -------- 54 -------- 41
                                -13/10        -13/10              equal
 

It's  B. experiment 2 that has a proportional relationship of temperature change over time

An inversely proportional relationship means that the decrease in temperature for the first 10 minutes equals the decrease in temperature for the second 10 minutes.

In Experiment 4, the temperature DROPS the same amount in each 10 minute interval.  That is called, “inversely proportional.”