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Algebra
Pregunta

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 $$T ( t ) = 69 \times ( \frac { 1 } { 2 } ) ^ { \frac { t } { 30 } } + 21$$ .

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