Question

Part 1 of 3A pizza pan is removed at 7:00 PM from an oven whose temperature is fixed at 450°F into a room that is a constant 71°F. After 5 minutes, the pizza pan is at 300°F.(a) At what time is the temperature of the pan 130°F?(b) Determine the time that needs to elapse before the pan is 170°(c) What do you notice about the temperature as time passes?(a) The temperature of the pan is 130°F at PM.(Do not round until the final answer. Then round to the nearest minute as needed.)

Answer 1

Step 1:

At t = 0 minute, the temperature is 450

`\begin{gathered} At\text{ t = 0 minute , the temperature is 450}^of \\ \text{At t = 5 minutes , the temperature is 300}^of \end{gathered}`
`\begin{gathered} \text{Rate of change, slope = }\frac{300\text{ - 450}}{5\text{ - 0}} \\ Slope\text{ = }(-150)/(5)\text{ = -30}^of\text{ min}^(-1) \end{gathered}`

Step 2

`\begin{gathered} \text{y = mx + c} \\ \text{y = -30x + 450} \\ \text{x is the time in minutes} \\ \text{y is temperature in }^of \end{gathered}`

a)

`\begin{gathered} \text{y = 130}^of\text{ , x = ?} \\ 130\text{ = -30x + 450} \\ 30x\text{ = 450 - 130} \\ 30x\text{ = 320} \\ \text{x = }(320)/(30) \\ \text{x = }(32)/(3) \\ x\text{ = 10minutes 40 seconds} \\ 7:10\text{ :40 pm} \end{gathered}`

b)