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Algebra
Pregunta

3. A hot cup of coffee cools according to the equa...

3. A hot cup of coffee cools according to the equation \( T ( t ) = 69 \times ( \frac { 1 } { 2 } ) ^ { \frac { t } { 30 } } + 21 \) where \( T \) is the temperature in degrees Celsius and \( t \) is the time in minutes. 

a) Is this an example of exponential growth or exponential decay? What part of the equation tells you that? [2] 

What is the initial temperature of the coffee? [1] 

c) After how many minutes is the temperature of the coffee \( 69.79 ^ { \circ } C \) . [4] 

d) Explain how the equation would change if the coffee cooled faster. [1] 

e) Explain the transformations (in the correct order) that the graph of \( T ( t ) = ( \frac { 1 } { 2 } ) ^ { t } \) undergoes to produce the graph of \( T ( t ) = 69 \times ( \frac { 1 } { 2 } ) ^ { \frac { t } { 30 } } + 21 \) . 

 

Answer

\(T(t)= 69\times 2^{\frac{- t}{30} } + 21\)

Solución
View full explanation on CameraMath App.