Question

ln(\frac{T - T_0}{T_i - T_0}) = -kt The given equation represents the logarithmic form of Newton's law of cooling, which states that the temperature $T$ of an object at time $t$ satisfies the given equation, where $T_0$ is the temperature of the object at time $t = 0$, $T_i$ is the object's surrounding temperature, and $k$ is a positive constant that depends on characteristics of the object. The temperature is measured in degrees Celsius ($^\circ C$), and time $t$ is in minutes. When a certain object is removed from an oven, it takes 30 minutes for the object to cool from 180$^\circ C$ to 30$^\circ C$ when the surrounding temperature is 20$^\circ C$. How many minutes would it take the same object to cool from 180$^\circ C$ to 30$^\circ C$ when the surrounding temperature is 24$^\circ C$? A 25.530 B 30.000 C 34.000 D 35.253

          ln(\frac{T - T_0}{T_i - T_0}) = -kt
The given equation represents the logarithmic form of Newton's law of cooling, which states that the temperature $T$ of an object at time $t$ satisfies the given equation, where $T_0$ is the temperature of the object at time $t = 0$, $T_i$ is the object's surrounding temperature, and $k$ is a positive constant that depends on characteristics of the object.
The temperature is measured in degrees Celsius ($^\circ C$), and time $t$ is in minutes. When a certain object is removed from an oven, it takes 30 minutes for the object to cool from 180$^\circ C$ to 30$^\circ C$ when the surrounding temperature is 20$^\circ C$. How many minutes would it take the same object to cool from 180$^\circ C$ to 30$^\circ C$ when the surrounding temperature is 24$^\circ C$?
A 25.530
B 30.000
C 34.000
D 35.253

ln((T - T0)/(Ti - T0)) = -kt
The given equation represents the logarithmic form of Newton's law of cooling, which states that the temperature T of an object at time t satisfies the given equation, where T0 is the temperature of the object at time t = 0, Ti is the object's surrounding temperature, and k is a positive constant that depends on characteristics of the object.
The temperature is measured in degrees Celsius (^∘ C), and time t is in minutes. When a certain object is removed from an oven, it takes 30 minutes for the object to cool from 180^∘ C to 30^∘ C when the surrounding temperature is 20^∘ C. How many minutes would it take the same object to cool from 180^∘ C to 30^∘ C when the surrounding temperature is 24^∘ C?
A 25.530
B 30.000
C 34.000
D 35.253

Added by Carlos C.

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