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A warm object cools according to the function T(t) = 331e-0.035t + 82. Assuming a constant environmental temperature, what constant temperature, in °F, will the object’s temperature eventually stabilize?
331°F
249°F
82°F
35°F

Respuesta :

Edufirst
Answer: 82.

The exponential part trends to 0 when time incresase towards infitinty, then for long times the function trends to 82.

Answer:

82

Step-by-step explanation:

example problem given:

A warm object cools according to the function T(t) = 95e-0.02t + 78.

The temperature T is a function of time t. The initial temperature of the object is given by T(0) = 173°F.

Looking at the end behavior of the function, 95e-0.02t will decay to 0 over time, so the temperature of the object will eventually stabilize to 78°F - the temperature of the room the object is in.

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