Problem

The financial analyst for a large construction fi…

02:36

Problem 76 Hard Difficulty

Use Newton's law of cooling to complete: $$T(x)=T_{R}+\left(T_{0}-T_{R}\right) e^{k x}$$
Newton's law of cooling applies equally well if the "cooling is negative," meaning the object is taken from a colder medium and placed in a warmer one. If a can of soft drink is taken from a $35^{\circ} \mathrm{F}$ cooler and placed in a room where the temperature is $75^{\circ} \mathrm{F}$, how long will it take the drink to warm to $65^{\circ} \mathrm{F} ?$ Assume $k \approx-0.031$.

Answer

44.719 minutes

Related Courses

Algebra

Precalculus

Chapter 4

Exponential and Logarithmic Functions

Section 2

Exponential Functions

Discussion

You must be signed in to discuss.

Top Algebra Educators

Watch More Solved Questions in Chapter 4

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5

Problem 6

Problem 7

Problem 8

Problem 9

Problem 10

Problem 11

Problem 12

Problem 13

Problem 14

Problem 15

Problem 16

Problem 17

Problem 18

Problem 19

Problem 20

Problem 21

Problem 22

Problem 23

Problem 24

Problem 25

Problem 26

Problem 27

Problem 28

Problem 29

Problem 30

Problem 31

Problem 32

Problem 33

Problem 34

Problem 35

Problem 36

Problem 37

Problem 38

Problem 39

Problem 40

Problem 41

Problem 42

Problem 43

Problem 44

Problem 45

Problem 46

Problem 47

Problem 48

Problem 49

Problem 50

Problem 51

Problem 52

Problem 53

Problem 54

Problem 55

Problem 56

Problem 57

Problem 58

Problem 59

Problem 60

Problem 61

Problem 62

Problem 63

Problem 64

Problem 65

Problem 66

Problem 67

Problem 68

Problem 69

Problem 70

Problem 71

Problem 72

Problem 73

Problem 74

Problem 75

Problem 76

Problem 77

Problem 78

Problem 79

Problem 80

Problem 81

Problem 82

Problem 83

Problem 84

Problem 85

Problem 86

Problem 87

Problem 88

Problem 89

Problem 90

Problem 91

Problem 92

Problem 93

Problem 94

Problem 95

Problem 96

Problem 97

Problem 98

Problem 99

Problem 100

Problem 101

Video Transcript

Okay, So noticed all this question We need to use the New England cooling. Um, So what we're doing here is we need to solve for X. Since that will give us the minutes it takes to get to t X peopling 65. So let's start with plugging in the values we know. So we know that we want the temperature tend of Equalling 65. Um, the surrounding temperature is 75. So bold Soon the initial temperatures and it's taken out. Um, that's seeking Out of it is 35 again, minus 75. And then we have he toothy negative. Zero point 031 times x. So we want to solve for this X right here. So what we can start doing is by subtracting 75 by both sides. Oh, that'll give us negative 10 on this side. We can even do 35 minus 75 to simplify this side, which is negative. 40. And then you can eat the negatives. Your point. See her 31 Thanks. And now what we want to do is, um, by both sides by negative 40 to isolate this e um, so we get 1/4 can be the negative 0.31 fax. So now, in order to isolate, um, this guy over here, we basically want to l and both sides, because when we Ln this the e basically canceled out since it's Helen E to the e. So what we will get is Ellen one for it cools negative. Zero 0.0 31 x So let's just people again. L enough. One worth real quick. So that's around negative. 1.38 feet six. And now we can just But I hear there divide pulls sides by negative 0.31 that we can isolate that X and then we get exp as 44 0.719 minutes and that will be your answer. That will be the amount of time it takes to get the temperature to 65 degrees.

We have video lessons for 91.91% of the questions in this textbook