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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 [tex]f(t) = Ce^{-kt} + 33[/tex] represents the situation, where [tex]t[/tex] is time in minutes, [tex]C[/tex] is a constant, and [tex]k[/tex] 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 :

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

- [tex]44.5[/tex]°C

Given that,

Function [tex]f(t)=Ce(-kt)+33[/tex]

where,

t = time in terms of minutes

C = constant

k = constant

The temperature of the object [tex]= 75[/tex]°

where, [tex]t = 0[/tex]

Using the function,

∵ [tex]f (0) = 75[/tex]

[tex]Ce^{(0)}[/tex] [tex]+ 33 = 75[/tex]

This will lead to

[tex]C = 42[/tex] (∵ C being constant)

Temperature post 2 minutes = [tex]55[/tex]°

or

[tex]55 =[/tex] [tex]42e^{(-2k)} + 33[/tex] (k being [tex]0.3233[/tex])

Thus,

Temperature after 4 minutes would be:

[tex]f(4) = 42e^{(-1.29325)} + 33[/tex]

[tex]= 44.5[/tex]°

Thus, [tex]44.5[/tex]°C is the correct answer.

Learn more about 'Temperature' here:

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Answer: 44.5

Step-by-step explanation:

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