An Object Cools at a Rate (Measured In ${ } ^ { \circ } \mathrm { C } / \mathrm { min }$

An object cools at a rate (measured in ${ } ^ { \circ } \mathrm { C } / \mathrm { min }$ ) equal to $k$ times the difference between its temperature and that of the surrounding air. Suppose the object takes 10 minutes to cool from 60 $^\circ$ C to 40 $^\circ$ C in a room kept at 20 $^\circ$ C. Find the value of $k$ .

A) $e ^ { - 20 }$
B) $\ln 2$
C) $10 e ^ { - 20 }$
D) $40 \ln 10$
E) $\frac { 1 } { 2 }$
F) $e ^ { - 1 / 20 }$
G) $\frac { 1 } { 10 } \ln \frac { 1 } { 2 }$
H) $60 \ln \frac { 1 } { 2 }$

Correct Answer:

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