- [Maximum mark: 6]
A cup of hot water is placed in a room and is left to cool for half an hour. Its temperature, measured in °C, is recorded every 5 minutes. The results are shown in the table.
| Time (mins) | 5 | 10 | 15 | 20 | 25 | 30 |
|---|---|---|---|---|---|---|
| Temperature (°C) | 59 | 52 | 46 | 40 | 35 | 29 |
Akira uses the power function T(t) = a tᵇ + 25 to model the temperature, T, of the water t minutes after it was placed in the room.
(a) State what the value of 25 represents in this context. [1]
(b) Use your graphic display calculator to find the value of a and of b. [3]
Soo Min models the temperature, T, of the water t minutes after it was placed in the room as T(t) = k cᵗ + 25.
(c) Find the value of k and of c. [1]
(d) State a reason why Soo Min’s model of the temperature is a better fit for the data than Akira’s model. [1]