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Question 135 PointsFrom a table inside a room with current temperature of 33 degrees Celsius, left over Fried Chicken is removed and placed inside refrigerator set ...

Question

Question 135 PointsFrom a table inside a room with current temperature of 33 degrees Celsius, left over Fried Chicken is removed and placed inside refrigerator set to temperature of 9 degrees Celsius. After 9 minutes the temperature of the chicken is 19 degrees Celsius. What is the temperature of the chicken 24 minutes after it was placed in the refrigerator? (use 2 decimal digit: unit is not needed)Add your answer

Question 13 5 Points From a table inside a room with current temperature of 33 degrees Celsius, left over Fried Chicken is removed and placed inside refrigerator set to temperature of 9 degrees Celsius. After 9 minutes the temperature of the chicken is 19 degrees Celsius. What is the temperature of the chicken 24 minutes after it was placed in the refrigerator? (use 2 decimal digit: unit is not needed) Add your answer



Answers

Use this scenario: A pot of boiling soup with an internal temperature of 100° Fahrenheit was taken off the stove to cool in a 69° F room. After fifteen minutes, the internal temperature of the soup was 95° F.

To the nearest degree, what will the temperature be after 2 and a half hours?

Toe. Hold the temperature of a room between 19 and 22 degrees Celsius. What Fahrenheit temperatures must be maintained. Let's start by writing a compound inequality that represents the temperature in degrees Celsius. The temperature is between 19 and 22 so we start with 19 is less than the temperature in Celsius is less than 22. Because we want the temperatures to maintain in degrees Fahrenheit, we're going to use the equation that the Celsius temperature is equal to five nights of the Fahrenheit minus 32. So we're gonna substitute the expression for Celsius into our compound inequality. We have 19 is now less than 5/9 of Fahrenheit temperature minus 32 which is less than 22. Let's start by multiplying all parts of our compound inequality by nine to get rid of the fraction nine times 19 is 171 is less than the nines will cancel out in our expression in the middle, leaving us with five times F minus 32 is less than 22 times nine, which is 198. Now. Let's rewrite the inequality without the parentheses, E and distribute five into F minus 32 we have 171 is less than five F minus 160 which is less than 198. Now. Toe. Isolate our five F in the middle of our compound inequality. Let's add 160 to all three parts of our inequality. This leaves us with 331 is less than five F is less than 358. The last step is to undo the product of five F and divide all three parts of the compound inequality by five, leaving us with 331 divided by five, which is 66.2 is less than F is less then 358 divided by five, which is 71.6. So our final answer to this question would be that the temperatures must be maintained between 66.2 and 71.6 degrees Fahrenheit between not equal to

Okay, were asked to calculate at T equal to five, but we need to convert us in minutes. So this is an I. R s O one hour is equal to 60 minutes. So are given Formula T of tea is equal to E for dirty money ln of 26 over 31 over 15 times T, which is 60 times 2.5 plus 69. If you focus in calculator, you get that This is approximately equal to send before Fahrenheit.

Newton's law of cooling question. Where even liquid that at time equals zero is currently five degree Celsius in a room that's 20 degree Celsius. We know a minute later that liquid is seven degrees Celsius. The question is, when is the liquid going to be 90% of the ambient temperatures in this case? Basically, what is the room party? When is it likely going to be essentially 90% of 20? In other words, when is there going to be 80 degrees Celsius? So you can recall from your text is a very nice condensed form of Newton's law of cooling. It's written this way. TFT, where T is in terms of minutes, equals a constant times E to the negative. Katie, which is another constant, plus your ambient temperature. Now, since we have two unknown Constance, we need to have to initial conditions which we do here and here. So I'm gonna first do issues. My first initial position to figure out see, is that we all that information to figure out K is and then we can work for us to figure out what time it is when the, um, like what is 18 degrees Celsius now, in this case, I think we think of Newton's law of cooling. We think it's something cooling down Okay, towards the temperature. In this case, this is a five degree Celsius initial temperature. The room temperatures 20. We're gonna actually be increasing, approaching, um, an upper threshold of 20 degrees. Keep that in mind. A little different than maybe I have a question that you've seen before. That's what. And jump into this. I'm gonna go ahead and start by plugging in five over here equals C times. You've probably seen this a whole bunch of times. You just kind of zero here because we have a negative case. You don't know times t which in this case is zero plus her ambient temperature, which is 20. And so we have negative 15 equal C and most examples you've seen before. See, it's positive, which allows then for the grafted behave the way it does for us. The negative here is gonna flip the graft. Normally, we're looking at a graph into something like this. It decays and approaches a value on the lower end. We're gonna negative C values was actually gonna change it. It's gonna flip it um, over. So we will actually be doing something on the lines of approaching an upper about. Okay, so we'll have a upper bound. This case is 20 versus a lower bound, which we've seen before way. Think of cooling. We think of a decreasing temperature. That is not to be the case. Just It's just approaching the equilibrium, which is going to be the ambient temperature. So if you start above the ambient temperature, you will be decreasing towards that. And if you start below the ambient temperature, you will be increasing towards that. But you will be increasing at a decreasing rate because he will be flattening out and approaching the asthma toe. Um, so we know that our see value is negative. 15. So we do know is well, using our other info, I could go and say this now seven equals negative 15 e to the negative K because we're looking at a value of one minute later. All right, And then that will be plus 20. So if we subtract 20 you get negative 13 which is gonna be then 13 15th equals e to the negative K Well, natural law both sides to cancel out the exponential, and we're left with a negative natural log of 13 15th people's. Okay. Okay. So what does that mean? It means our general equation is gonna look like this Negative 15 he raised. Now the negative here and the negative. And the equation. We're gonna cancel, and you're gonna be left with the rays to the natural log of 13 15th T plus 20. I like to keep my k value these act. So the natural log of 13 15th is roughly negative. 0.14 Okay, but I want to make sure now that I don't use a estimated value for something I'm looking for, so I dont round to the very end. Okay, so now I want to know when are we gonna be equal to 80 degrees? So I'll take this equation and check it up here. I want to know what am I gonna b e t 18 equals naked 15 e to the natural log of 13 15th T plus 20. That's going to get us to 15th. You're gonna 18. Minus 20 s negative too. And the new environment Negative. 15. So you're positive to 15th people's e races? Natural log 13 15th t You will have to natural log again on both sides. Um, these don't cancel out because of the tea sitting here. So what, you'll have Pardon me to the back. What I meant was, these don't cancel out. Of course these will. So you're left with the natural log of to 15th equals the natural log of 13 15th t Or in other words, the natural log of to 15th divided by the natural log of 13 15th. And that equals your T value. And of course, I would never use that value to talk to somebody. Um, because they wouldn't probably understand financial like up to 15 divided by the natural Argo 13 15 cents. So if we go ahead and at this point now, allow us to round since we're finally done land of with a value that's roughly 14 so it can take roughly part me roughly 14 minutes for this'll liquid. That was initially five degrees to become 18 degrees

Given the fact that the top of their mom better originally re 72 fair and heights and after being placed in a refrigerator, the temperature is a constant 38 up in the refrigerator, so outside versus in the fridge and for party were given the information that throw Momma. Her reads 60 F after two minutes of being in the refrigerator. So two minutes we can set up a function logistic model of the decay of the temperature or decline of temperature. Where and if T is the temperature of the thermometer. Basically sequel to the starting temperature. Times E Raise The power of K Times team Ortiz, Time and K is the rate of the decline of temperature. So after two minutes, the temperature read 60 60 equals 72 is irrational. Two. Que two is the temperature. We're looking for K five votes size by 72 and we have, um, succeeds about by Sony to take the natural log of both sides and now divide both sides by two. So natural log of 60 divided by 72 defined by two, is negative nine point negative 0.91 to use this number K and were asked how long what it will it read after seven minutes. So we're gonna find end of seven and a t any t seven times seven t? You can actually plugged us into a calculator. So 72 times E race The negative 0.912 times seven is approximately 38.0 to 6. So approximately 38 F It's after seven minutes and part B were asked, um were asked to find the time until the temperature reads 45 degrees. So 45 is here. We're about equal. So sorry. Mount's still 72 times T We're looking for tea here. I want to take the natural log of both sides to get naturalized. 45 72 go to negative 0.912 t divide both sides by negative 0.120912 And so you take natural log of 45 divided by 72 and divide that number by native 0.912 and we get approximately 39.17 So temperatures about 39.17 Fahrenheit degrees and part C we're asked, um, so apart were asked to find the amount of time Um oh, actually makes up part B and C. This should be part see, and Part B is asking for the amount of time until the temperature reads 39 degrees. So just one degree above the degree of the refrigerator. You said the same process as we did and see Divide both sides by 72 and take the natural log on both sides. It's a natural log of e is just getting rid. The use of is equal to the power Times t. And now we just divide the natural log of 39 divided by 72 by negative 0.912 and this proximately equal to 6.72 three six my sons to three minutes approximately. And as we can see, um, the time decreases quite quickly and two minutes in two minutes. Eat it. Decreases uh, from 72 to 60 and from, uh, in one minutes over here from part B to part C in one minute we see from sick or from 6.723 minutes to seven minutes. It decreases by approximately Ah, one degree or less than one degree. And for part A. We see that with seven minutes, it takes its around. When you leave the driver in the fridge for seven minutes, it's 38 degrees. And when you leave the thermometer fridge for 6.7 degrees, it's 39 degrees of, um, you see US time increases. As time increases, temperature decreases more slowly, so it's a little something like this. With the slope decreases. As export time increases, the value increases here.


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