Question

A solid object with an initial temperature of 75 degrees Fahrenheit is dropped into a lake with a temperature of 33 degrees Fahrenheit. The function f(t)=Ce(−kt)+33 represents the situation, where t is time in minutes, C is a constant, and k is a constant.

After 2 minutes the object has a temperature of 55 degrees. What will be the temperature of the object, in degrees Fahrenheit, after 4 minutes? Round your answer to the nearest tenth, and do not include units.

Answer 1

Answer: 44.5

Step-by-step explanation:

Answer 2

The object's temperature post 4 minutes in respect to degrees Fahrenheit would be:

- $44.5$°C

Given that,

Function $f(t)=Ce(-kt)+33$

where,

t = time in terms of minutes

C = constant

k = constant

The temperature of the object $= 75$°

where, $t = 0$

Using the function,

∵ $f (0) = 75$

$Ce^{(0)}$ $+ 33 = 75$

This will lead to

$C = 42$               (∵ C being constant)

Temperature post 2 minutes = $55$°

or

$55 =$ $42e^{(-2k)} + 33$                (k being $0.3233$)

Thus,

Temperature after 4 minutes would be:

$f(4) = 42e^{(-1.29325)} + 33$

$= 44.5$°

Thus, $44.5$°C is the correct answer.

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