Question

1. a baker records the internal temperature of a pie that has been left to cool on a counter. the room temperature is 14°c. an equation that models this situation is (t(t)=68(0.5)^{\frac{t}{10}} + 14) where (t) is the temperature in degrees celsius and (t) is the time in minutes. a) determine the temperature, to the nearest degree, of the pie after 30 minutes. 3a

Explanation:

Step1: Substitute t value

Substitute $t = 30$ into $T(t)=68(0.5)^{\frac{t}{10}}+14$.
$T(30)=68(0.5)^{\frac{30}{10}}+14$

Step2: Calculate exponent

First, calculate $(0.5)^{\frac{30}{10}}=(0.5)^3$.
$(0.5)^3 = 0.5\times0.5\times0.5=0.125$

Step3: Calculate multiplication

Then, calculate $68\times(0.5)^3 = 68\times0.125 = 8.5$

Step4: Calculate final temperature

Finally, calculate $T(30)=8.5 + 14=22.5\approx23$

Answer:

$23^{\circ}C$