Question

when a temperature of a pot in a kiln is 1,200°f, an artist turns off the heat and leaves the pot to cool at a controlled rate of 81°f per hour. express the temperature of the pot in degrees celsius as a function of the time t (in hours) since the kiln was turned off. (c ∘ f)(t)=

Explanation:

Step1: Find the temperature in Fahrenheit as a function of time

The initial temperature is $1200^{\circ}F$ and it cools at a rate of $81^{\circ}F$ per hour. So the temperature in Fahrenheit $F(t)$ as a function of time $t$ (in hours) is $F(t)=1200 - 81t$.

Step2: Use the conversion formula from Fahrenheit to Celsius

The conversion formula from Fahrenheit $F$ to Celsius $C$ is $C=\frac{5}{9}(F - 32)$. Substitute $F(t)$ into the conversion formula:
\[

$$\begin{align*} (C\circ F)(t)&=\frac{5}{9}((1200 - 81t)- 32)\\ &=\frac{5}{9}(1168 - 81t)\\ &=\frac{5\times1168}{9}-\frac{5\times81t}{9}\\ &=\frac{5840}{9}- 45t \end{align*}$$

\]

Answer:

$\frac{5840}{9}-45t$