Question

Jessie just finished the probation period at work and got a $0.50 per hour raise and 4 more hours of work per week. Jessie's friend scoffed, “That's only $2 more per week! Who cares?” Why is Jessie's friend wrong about the change in Jessie's weekly pay? What more do we need to know about Jessie's work situation to calculate the actual change in the pay? How is this related to the product rule in calculus class?

Answer 1

Jessie's friend isn't very good at math is he?

Answer 2

You're in calculus?

Answer 3

Apparently not. And yes.

Answer 4

This seems incongruous. An algebra question teamed up with one on calculus. What the biggest mistake that the friend is making?

Answer 5

The friend isn't taking into account how much Jessie is getting paid in the first place, right? This is the first written problem I have been given in this class so I'm a little confused.

Answer 6

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Answer 7

@goformit100 We're chatting about the subject. This is Open STUDY isn't it. Isn't that how you study with other people?

Answer 8

@kmchargue Right. He only took into account the raise she recieved.

Answer 9

So the new pay per week would be written as xy+0.5x+4y+2 and the increase as 0.5x+4y+2 but how would you write in words how it relates to the product rule?

Answer 10

Hold on, I ha

Answer 11

Okay. So you're confidant that you have the right equation?

Answer 12

If you are, we can begin turning it into words.

Answer 13

The next part is a snap, isn't it? Just take another look at the question.

Answer 14

@kmchargue You still there?

Answer 15

@goformit100 Great. It looks like you scared her off. :(

Answer 16

I'm here i'm here. Sorry. I believe that would be the right equation but of course I could be wrong.

Answer 17

Okay. Good. I'd like to learn more about all of this stuff. I've seen the Product Rule explained, but I don't really remember it right now. Can you help me out, while I'm helping you?

Answer 18

Looks good to me, but you can always doublecheck with someone. After all, you're clearly not someone who wants other people to do her homework for her.

Answer 19

it's the product of the first function and the derivative of the second function plus the product of the derivative of the first function and the second function

Answer 20

Ah, I remember that now. I wonder how in the world that relates to this. Haha. Really. I don't get it?

Answer 21

Neither do I. I'm just lost haha.

Answer 22

There's some connection. We just need to figure out what it is. It's in there. We'll get it.

Answer 23

What is expected in the answer is given as well as


Answers: A complete answer to the middle paragraph should explain what Jessie's friend did and why it is wrong (by a lot) in plain, common sense, English. This will almost certainly already include an indication of what further information is needed, but if not that should be included as well.

A complete answer to the last paragraph will state the product rule, describe the relation of the derivative to the change, describe how the weekly pay is a product and how the product rule works in this case. An A-level answer will compare this calculus method to the direct calculation, using some made-up but reasonable values for the missing information.

Answers that are not written at the college level, for instance, answers not using complete sentences, will be assigned a failing grade.

Answer 24

"to calculate the actual change" in the pay? How is this related to the product rule in calculus class?

Answer 25

So, change and calculus. We're onto something there.

Answer 26

Oh, the full question helps. A LOT. :)

Answer 27

It's a start haha

Answer 28

"Answers that are not written at the college level, for instance, answers not using complete sentences, will be assigned a failing grade."

YIKES!!! Tough teacher.

Answer 29

Well, what do you say we right out in words what we know right now. That will give us some confidence, I HOPE. Haha

Answer 30

Ok that works haha.

Answer 31

"A complete answer to the middle paragraph should explain" What's he/she mean by middle paragraph.

Answer 32

The first piece of the puzzle that you would need is the amount of hours Jessie works per week. Jessie will not be making just 2 more dollars a week he would also be getting an additional 50 cents for each hour that he is working. The product rule is d/dxf(x)g(x)=f′(x)g(x)+f(x)g′(x)

Answer 33

Is the first paragraph the initial situation?

Answer 34

Yeah for some reason it didn't separate into paragraphs when I posted it on here

Answer 35

No, I mean the instructions seem to indicate that this should be in the middle paragraph, or am I confused about that?

Answer 36

Why is Jessie's friend wrong about the change in Jessie's weekly pay? What more do we need to know about Jessie's work situation to calculate the actual change in the pay?

was considered the "second or middle" paragraph

Answer 37

I admire the way you're going about this. So many people wait until the last instance to begin. You've given yourself plenty of time. Plas, it might really help with future problems you come across.

Answer 38

So it's just saying a complete answer to what it's asking there

Answer 39

Well, maybe we should go about it that way in any event. Know what I mean. Set it up, and then explain why the guy is wrong. Then lastly, explain how it is related to the Product Rule.

Answer 40

That sounds like the best way to go about it

Answer 41

So, the first paragraph would be something like this, it seems to me--

Jessie received a $0.50 per hour raise as well as 4 more hours of work per week. Yet, her friend thinks she is only making two more dollars a week. Here's why her friend is wrong.

Answer 42

Then the next paragraph will explain in order why he's wrong.

Answer 43

Do you feel up to giving that one a shot?

Answer 44

How about we both work on it seperately, and we can compare paragraphs?

Answer 45

Jessies' friend isn't taking into account all of the required information. For one thing, he's overlooking the fact that the raise applies to her entire salary, and not simply the additional four hours she is getting.

Answer 46

Alright that'll do

Answer 47

That's what I have as well

Answer 48

Jessies' friend isn't taking into account all of the required information. He's overlooking the fact that the raise applies to her entire salary, and not simply the additional four hours she is getting.

Answer 49

Okay. What next?

Answer 50

Describe the relation of the derivative or the original pay to the change, describe how the weekly pay is a product and how the product rule works in this situation

Answer 51

Good. Better might be a segue into the Product Rule. But let's leave that for later.

Answer 52

Since calculus is all about rates of change, we have to include that.

Answer 53

Yes, I was just about to mention that

Answer 54

There's the unkown amount of what she initially made, but that's not a problem--I think. Because wouldn't the rate of change be simllar? perhaps in the same family of functions?

Answer 55

Actually, since you know more about this than I do, you should make the final decision. Although I am decently good at English.

Answer 56

Putting it into words hopefully won't be too much of a struggle. All I really need to do now is plug in some reasonable numbers for the missing information and work out the equations using the product rule.

Answer 57

You knw, km, being on Open Study here for alomost two weeks now has been a humbling experience for me. I'm realizing just how much stuff I DON'T know. :(

Answer 58

Okay. Hold on. I'll find someone who can help you without doing it for you. I know some people here who are like that. Hold on.

Answer 59

Be right back.

Answer 60

Ok thank you so much

Answer 61

Ok, new Open Study friend. I think I'll have a calculus expert here shortly.

Answer 62

In the meanwhile, have you ever watched Futurama?

Answer 63

Because Jessie's friend seems about as smart as Fry. :)

Answer 64

Hahaha yes

Answer 65

Love that Bachelor Chow. Yummy.

Answer 66

Here's the link to those textbooks I mentioned. It'll save you lots of money. Or your parents, anyway. :)

http://opencoursescholar.wordpress.com/resources/openstax-textbooks/

Answer 67

Ok thank you :)

Answer 68

If we do any more studying together on any subject, it will be nice to work from the same textbook.

Answer 69

Of course

Answer 70

What's next on your academic agenda? What classes are you taking?

Answer 71

Business writing, marketing, econ, terminology

Answer 72

Lots to do

Answer 73

Ah, economics. I'm reading "Wealth of Nations" right now. You really should read it. It's never taught in school, even though it's one of the best books of all time. You know how with some books you need to get a commentary to understand it? . . .

Answer 74

Yes

Answer 75

You don't need a commentary for this book. It's filled with straightforward really interesting sentences. Absolutely HIGHLY recommend it!!!!

Answer 76

I think someone will be here shortly.

Answer 77

@goformit100 We need a calculus expert and can't seem to find one right now. Can you help?

Answer 78

I hope so!

Answer 79

I have an idea. What if I laced the same question up. Then you could have what we've done here and a new one for someone to come across. (They only let you ask one question at a time.)

Answer 80

Yes that will work!

Answer 81

Okay. Its at the top of the list, and someone is looking it over now.

Answer 82

Why not just bump the question lol

Answer 83

I'm new to all this. Not quite sure what I'm doing.

Answer 84

Because it has such a long discussion on it.

Answer 85

Try this discussion: http://openstudy.com/study#/updates/5271aa24e4b077aaee83f022

Answer 86

I'm really feeling bad that you aren't getting the help you need. You deserve it. You're a very good student.

Answer 87

@kmchargue Just follow @tkhunny 's link theres the answer

Answer 88

Thank you. I'll get in eventually.

Answer 89

@GirlByte No kidding. How'd that happen?

Answer 90

I saw that. But it mentions how the comparison doesn't add up so I was confused.

Answer 91

it needs to be set up in equation form so if we set
x=original hours worked
y=original new per hour
xy=overall pay
new pay= (x+4)(y+0.5)
= xy+.5x+4y+2
increase= 0.5x+4y+2

but how to relate that to the product rule??