A thermometer is taken from a room where the temperature is 20◦C to the
outdoors, where the temperature is 5◦C. After one minute the thermometer reads 12◦C.
(a) What will the reading on the thermometer be after one more minute?
(b) When will the thermometer read 6◦C?

a) : at time t = 2 minutes the temperature will be 8.265 degress

b) : the temperature will be 6 degrees at time t = 3.55 minutes.

Step-by-step explanation:

When dealing with temperature changes, it's best to work with Newton's Law of Cooling.

here:

: the temperature in the room.

: ambient (or outdoor) temperature (that always remains constant, in our case: )

: are constants

Our conditions are provided:

1)

2)

using the first condition

using the second condition:

we can use our calculated value of C to find k

Finally we can put these constants back in the main equation:

or

a) Reading after one more minute?

so it's asking:

T(2) = ?

Hence, after one more minute the temperature of the room will be 8.267 degrees

b) When will it be 6 degrees?

T(t) = 6?

Hence at t = 3.55 minutes the temperature of the room will be 6 degrees.