A thermometer reading 7 degrees C is brought into a room with a constant temperature of 29 degrees C.

If the thermometer reads 15 degrees C after 4 minutes, what will it read in 6 minutes? 11 minutes?

To answer this question, we need to understand how the thermometer reading changes over time when brought into a room with a constant temperature.

The thermometer follows a pattern of approaching the room's temperature gradually. This pattern is described by Newton's law of cooling, which states that the rate of change of temperature is proportional to the difference between the object's temperature and the surrounding temperature.

In our case, the initial temperature of the thermometer is 7 degrees C, and the surrounding temperature is 29 degrees C. We can write this relationship using the following equation:

dT/dt = k(T - Ts)

Where:
dT/dt = rate of change of temperature
k = proportionality constant
T = temperature of the thermometer
Ts = surrounding temperature

The solution to this differential equation is given by:

T(t) = Ts + (T0 - Ts)e^(-kt)

Where:
T(t) = temperature of the thermometer at time t
T0 = initial temperature of the thermometer

Now, let's calculate the value of k using the given information:

T(4) = 15 degrees C
T0 = 7 degrees C
Ts = 29 degrees C
t = 4 minutes

15 = 29 + (7 - 29)e^(-k * 4)
-14 = -22e^(-4k)
e^(-4k) = 14/22
e^(-4k) = 7/11

Taking the natural logarithm (ln) on both sides:

-4k = ln(7/11)
k = -ln(7/11) / 4

Now we can use this value of k to calculate the temperature of the thermometer at any given time.

For t = 6 minutes:

T(6) = 29 + (7 - 29)e^(-k * 6)

For t = 11 minutes:

T(11) = 29 + (7 - 29)e^(-k * 11)

Calculating these values will give you the temperature readings of the thermometer at 6 minutes and 11 minutes.

There has to be more to this question.

Are we to assume Newton's Law of "Cooling" or
are you assuming the change is linear ?

If linear, then it changed 8° in 4 min, or 2° per minute
so after 6 minutes, it would change 12° to read 19°
after 11 minutes, it would change 22° and read 29° which was the original room temperature.

Such a change would not happen in reality, it would follow the laws discovered by Newton, and would require Calculus.