You arrive home to find your power is out. Your brother says...

You arrive home to find your power is out. Your brother says the freezer still feels cold, so it is okay to cook a frozen steak. You measure the temperature with a freezer thermometer. It reads $3^{\circ} \mathrm{C}$. Dad says that the steak is okay to cook today. Mom says to throw it out. What temperature is the freezer using customary measurement (the Fahrenheit scale)? What should you do with the steak?

Key Concepts

Temperature Conversion

This concept involves converting a measurement in degrees Celsius to degrees Fahrenheit using the formula F = (C × 9/5) + 32. In this scenario, converting 3°C yields approximately 37°F. This calculation is essential for comparing temperature readings to customary standards in regions that use the Fahrenheit scale.

Food Safety Guidelines

This concept emphasizes the importance of storing perishable food items at safe temperatures. Freezers are typically maintained at or below 0°F to slow bacterial growth and preserve food quality. A freezer reading of 37°F indicates that the temperature is far above the safe threshold, which can allow bacteria to proliferate. Thus, using or cooking meat that has been stored at this temperature is unsafe, and it should be discarded.

Transcript

00:01 We are problem number 50 which is related to the newton's law of cooling.

00:04 So let us get an idea about newton's law of cooling, which says t equal to c plus t0 minus c, t0 minus c, e -d is to the power k t where t is the temperature after time t, temperature of the object after time t, t -not is initial temperature of the object.

00:29 This is temperature of the object after time t initial temperature of the object after time t this is the constant temperature of the surrounding constant temperature of the surrounding k is any negative constant so in our question it is being given that initial temperature is 24 degree fahrenheit so t not equal to 24 degree fahrenheit room temperature that is a constant temperature c equal to 65 degree fahrenheit after 10 minutes that is t equal to 10 after 10 minutes temperature has risen to 30 degree fahrenheit so t equal to 30 degree fahrenheit so let us plug in everything here in equation number one that is the model it will be t that is 24 equal to c that is 65 plus t not that is 24 minus 65 this is this has to be 30 degree okay 30 30 it is to the power k t okay let us subtract both sides are 65 so this will become minus 35 equal to minus 41 a raise to the power k t let us divide both sides by minus 41 it will be getting minus 35 by minus 41 equal to e to power k t so if you write other way around it will become a greater of power k t equal to 35 by 41 since e is involved and we have to find the value of k and t should be equal to 10 minute as it was being given so it will be ln e raise to the power 10k equal to ln 35 by 41 so 10k lene equal to ln 35 by 41 okay this is 35 is correct yes now ln e is 1 so k will be equal to ln 35 by 41 divided by 10 so ln 35 by 41 divided by 10 so it's 0 minus 0 .0158.

03:11 Minus 0 .0158.

03:15 So this is the value for k...

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