A thermometer reading 7degreesC is brought into a room with a constant temperature of 30 degrees C. If the thermometer reads 16degreesC after 2 minutes, what will it read after being in the room for 4 minutes? For 9 minutes?

a) u (x) = 21.47°C

b) u (x) = 27.53°C

Explanation:

This requires Newton's Law of Cooling. The formula is:

u (x) = T + (T₀ - T) * e^ (kt)

Plugging in our information:

u (x) = 30 + (7 - 30) * e^ (kt)

u (x) = 30 - 23*e^ (kt)

at temperature 16°C at time 2 min.

16 = 30 - 23*e^ (2 k)

e^ (2k) = 14/23

2k = ln (14/23)

k = - 0.248

Temperature at t = 4 minute

u (x) = 30 - 23*e^ (-0.248*4)

u (x) = 21.47°C

temperature at t = 9 min

u (x) = 30 - 23*e^ (-0.248*9)

u (x) = 27.53°C