When an object is removed from a furnace and placed in an environment with a constant temperature of 62 °F, its temperature is 1620 °F. One hour after it is removed, the temperature of the object is 1184 °F. Find the temperature of the object 6 hours after the object is removed from the furnace. (Round your answer to 2 decimal places.)

after 6 hours the temperature of the object will be 297.33 F

Step-by-step explanation:

We can use Newton's Law of Cooling:

here,

: The temperature that of the object (that is changing)

: Temperature of the surroundings (that is not changing) = 62

: time (in unit hours)

: Are constants.

In our case were given two conditions:

: at time t = 0, the temperature of the object is 1620

and

: at time t = 1, the temperature of the object is 1184

we're going to use these conditions to find the values of C and k

using the first equation:

using the second equation

Putting these values back in the original equation:

considering the 'ln' and 'e' cancel out, this can also be written as:

Now we need to find what the temperature of the object will be at 6 hours.

after 6 hours the temperature of the object will be 297.33 F

1/3 + 1/3 ≠ 2/6 because 1/3 alone = 2/6  

step by step explanation:

1/3 + 1/3 = 2/3       2/3=4/6