Question
Asked Oct 1, 2019
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An object is heated to 191"F and is then allowed to cool in a room whose air temperature is 60 F. The
temperature u of the object t minutes after being placed in the room is given by
u(t) = 60+131e 0.0275e
(a) What will the temperature of the object be after 7 mninutes?
(b) How long will it take until the temperature of the object is 69 F?
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An object is heated to 191"F and is then allowed to cool in a room whose air temperature is 60 F. The temperature u of the object t minutes after being placed in the room is given by u(t) = 60+131e 0.0275e (a) What will the temperature of the object be after 7 mninutes? (b) How long will it take until the temperature of the object is 69 F?

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Expert Answer

Step 1

Given:

‘u’ is the temperature and ‘t’ is time

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u(t) 60+131e0.0275

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Step 2

Part (a)

Here, put t = 7

So, temperature of the object after 7 minutes:

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(t)= 60131e-0.0275 u(7) 60131e-0.0275<7 u(7) 60 131e-0.1925 u(7) 60 131x0.8284 u(7) 60 108.52 u(7) 168.52

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Step 3

Part (b)

Put u (t) = 69

So, the time it takes until t...

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ut)=60131e-0.0275 69 60 131e-0.0275 69-60 131e0.0275; 9 131e0.0275 -0.0275 6 131 0.068 e-0.0275 In(0.068) 0.0275t -2.6882 0.0275t 2.6882 t = 0.0275 t =97.75 98min

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