Solve the Problem $T ( t )$ Is Modeled By $T ( t ) = T _ { a } + \left( T _ { 0 } - T _ { a } \right) e ^ { - k t }$

question 114

Multiple Choice

Solve the problem.
-Newton's law of cooling indicates that the temperature of a warm object will decrease exponentially with time and will approach the temperature of the surrounding air. The temperature $T ( t )$ is modeled by $T ( t ) = T _ { a } + \left( T _ { 0 } - T _ { a } \right) e ^ { - k t }$ . In this model, $T _ { a }$ represents the temperature of the surrounding air, $T _ { 0 }$ represents the initial temperature of the object and $t$ is the time after the object starts cooling. The value of $k$ is the cooling rate and is a constant related to the physical properties of the object.
A cake comes out of the oven at $335 ^ { \circ } \mathrm { F }$ and is placed on a cooling rack in a $70 ^ { \circ } \mathrm { F }$ kitchen. After checking the temperature several minutes later, it is determined that the cooling rate $k$ is $0.050$ . Write a function that models the temperature $T ( t )$ (in ${ } ^ { \circ } \mathrm { F }$ ) of the cake $t$ minutes after being removed from the oven.

• A) \(T ( t ) = 335 + 70 e ^ { 0.050 t }\)
• B) \(T ( t ) = 70 + 265 e ^ { 0.050 t }\)
• C) \(T ( t ) = 70 + 265 e ^ { - 0.050 t }\)
• D) \(T ( t ) = 70 + 335 e ^ { 0.050 t }\)

Understand the concept and implications of the flexible self in contemporary society.

Comprehend the processes and outcomes of socialization in adolescent peer groups.

Grasp the significance and emergence of childhood and adolescence as distinct life stages.

Differentiate between and understand the roles of significant other and generalized other in social development.

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