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)^(t/10)+14 where t is the temperature in degrees celsius and t is the time in minutes after the pie has been left to cool. a) determine the temperature, to the nearest degree, of the pie 30 minutes after it has been left to cool.

Explanation:

Step1: Identify the given formula

The formula for the temperature $T(t)=68(0.5)^{\frac{t}{10}}+ 14$, where $t$ is time in minutes.

Step2: Substitute $t = 30$

We need to find the temperature when $t = 30$. Substitute $t=30$ into the formula: $T(30)=68(0.5)^{\frac{30}{10}}+14$.

Step3: Simplify the exponent part

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

Step4: Calculate the product part

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

Step5: Calculate the final temperature

Now, $T(30)=8.5 + 14=22.5\approx23$.

Answer:

23