Question

4.) The temperature of a food in a freezer has been shown to decrease by 1.7% each minute.a.) If a chicken breast is put in the freezer with a current temperature of 190 degreesFahrenheit, what will be the temperature after 20 minutes?b.) How long after you place the chicken breast in the freezer will it be frozen? (use graph)

Answer 1

Given:

Rate of decrease each minute = 1.7% = 0.017

Let's solve for the following:

• (a). Given:

Initial temperature = 190 degrees

Let's find the temperature after 20 minutes.

Apply the exponential decay formula:

`y=a(1-r)^t`

Where:

t is the time in minutes = 20 mins

a is the initial temperature = 190 degrees

r is the decay rate = 0.017

The equation below represents this situation:

`y=190(1-0.017)^t`

Plug in values into the formula and solve for y.

We have:

`\begin{gathered} y=190(1-0.017)^(20) \\ \\ y=190(0.983)^(20) \\ \\ y=190(0.70969) \\ \\ y=134.84 \end{gathered}`

Therefore, the temperature after 20 minutes will be:

134.84 degrees Fahrenheit.

• (b). How long after you place the chicken breast in the freezer will it be frozen?

We have the graph below:

The chicken will get frozen when the temperature gets to 0 degrees.

From the graph, it will get frozen at 750 minutes

ANSWER:

• (a). 134.84 degrees Fahrenheit

,

• (b). 750 minutes.