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Mathematics 15 Online
OpenStudy (anonymous):

Will give you a medal! Please help. 1.)E.J. has shown that a function, f(x), grows by 12% for every unit in the domain. What does this prove? a. The function f(x) is an arithmetic sequence. b. The function f(x) is a geometric sequence. c.The function f(x) is not a sequence. d. This does not prove anything. 2.)Fiona has proved that a function, f(x), is an arithmetic sequence. How did she prove that? She showed that an explicit formula could be created. She showed that a recursive formula could be created. She showed that f(n) ÷ f(n - 1) was a constant ratio. She showed that f(n) - f(n - 1) was a constant difference. 3.)Isaac keeps track of the miles per gallon his car gets per week. He has accumulated the following data: (1, 24), (2, 24.48), (3, 24.97), (4, 25.47) What is the common difference or ratio? The common difference is 0.48. The common difference is 0.50. The common ratio is 0.98. The common ratio is 1.02. 4.)Zach read a book for 10 minutes every weekend in the first month, 20 minutes in the second month, 40 minutes in the third month, and 80 minutes in the fourth month. Victoria read a book for 35 minutes every weekend in the first month, 50 minutes in the second month, 65 minutes in the third month, and 80 minutes in the fourth month. Which statement best describes the methods used by Zach and Victoria to increase the time they spent reading a book? a. Zach's method is linear because the number of minutes increased by an equal factor every month. b. Victoria's method is linear because the number of minutes increased by an equal number every month. c. Both Victoria and Zach's method is exponential because the number of minutes increased by an equal factor every month. d. Both Victoria and Zach's method is exponential because the number of minutes increased by an equal number every month. 5.)A store had 250 bottles of water. Each week, 40% of the bottles were sold and 48 new bottles arrived in shipments. Which recursive function best represents the number of bottles of water in the store? a. f(n) = f(n - 1) • 0.4 + 48, n > 0 b. f(n) = 250 - f(n - 1) • 0.4 + 48, n > 0 c. f(n) = f(n - 1) • 0.6 + 48, n > 0 s. f(n) = 250 - f(n - 1) • 0.6 + 48, n > 0

OpenStudy (anonymous):

@Easyaspi314 Can you help me with any of these? :O

OpenStudy (anonymous):

1) If something grows by a certain percent for every unit, then that is a geometric sequence. For example, if money is compounded 6% annualy, then thats a geometric sequence or geometric growth.

OpenStudy (anonymous):

2) If you have a sequence, like 3,7,11,15, .... cuch that the second term - first term is the same as the third term - second term, then that sequence is an arithmetic sequence. In my example, 7-3 = 4; 11-7 = 4, 15-11 = 4, the common difference is 4, so it makes that sequence an arithmetic sequence. And f(n) - f(n-1) has the same difference.

OpenStudy (anonymous):

3) I really don't like the third question. It is very poorly worded. There really is no common difference...as you can see it goes from 24 to 24.48 to 24.97...there is no common difference. It has a similar common ratio, approximately 1.02, but not exactly 1.02 for all of them. So I'm a bit troubled with the wording of that question.

OpenStudy (anonymous):

there?

OpenStudy (anonymous):

yes i am here :) I was trying to read question 3 to see if i could understand it myself, but you're right it doesn't make much sense

OpenStudy (anonymous):

In #3, we usually dont find common differences/ratios in coordinates; but it can be done. But it is inconsistent. But a common ratio of 1.02 is pretty close. Not exactly 1.02.

OpenStudy (anonymous):

Ahh ok i see! i need to know that for future references, because that question was confusing

OpenStudy (anonymous):

#4) Look at the Zach's reading: 10,20,40,80 Look at Victoria's reading: 35,50,65,80 In Zach's reading, everyth number is doubled by 2..so 10 x 2 = 20...20 x 2 = 40....40 x 2 = 80. That doubling is called exponential. In Victoria's reading: every reading is increased by 15...35 + 15 = 50....50 + 15 = 65....65+15 = 80. So there is this constant and same increase in numbers...so that is an arithmetic sequence (what we talked about in #2)...and the arithmetic sequence is a linear graph...or the graph of a straight line.

OpenStudy (anonymous):

So which choice do you see correct for #4?

OpenStudy (anonymous):

so im thinking the answer is D

OpenStudy (anonymous):

correct? :0

OpenStudy (anonymous):

No. D says that both are exponential. Thats not true. Look at what I typed earlier that Victoria is linear as it increases by the same number of minutes..always increases by a constant 15 minutes.

OpenStudy (anonymous):

Look at B. Is that correct?

OpenStudy (anonymous):

B, because her minutes increased

OpenStudy (anonymous):

yes, it increased by the same number of minutes. Interesting, that choice B doesnt talk about Zach's method.

OpenStudy (anonymous):

Yes B. Because c doesn't make sense and neither does A

OpenStudy (anonymous):

#5 is quite extensive.........

OpenStudy (anonymous):

See thats why i thought the answer was D because i was thinking thAt we had to find an answer for both methods! lol

OpenStudy (anonymous):

It's okay if you don't want to try it :) I got it from here, thank you so much! you're my favorite helper on here because you actually explain the problems to me :)

OpenStudy (anonymous):

You can try #5.......it's not difficult..but I want you to understand what is happening in that question.

OpenStudy (anonymous):

Alright how do i start it out?

OpenStudy (anonymous):

Take a few moments to read and understand what is being stated and asked.

OpenStudy (anonymous):

Alright so each WEEK 40 percent of the water bottles were being sold. Then 48 new bottles of arrived

OpenStudy (anonymous):

So the problem is asking us to find the correct function that represents how many bottles of water are now in the store? right?

OpenStudy (anonymous):

Yes...and the best way for you to see what's happening is to compute for the first 2 or 3 weeks...the # of bottles of water in the store... So let's see: In week #1: start off with 250 bottles, they sell 40% of the 250 which is 100...so they are left with 150 bottles...and they get a delivery of 48 bottles...so in week #1, they have 250 - 100 +48 Agree with week # 1?

OpenStudy (anonymous):

Yes i agree

OpenStudy (anonymous):

So in week #1...they have 198 bottles in stock. That is 250 - 100 + 48 OR we can say that they have 250 - 40% of the 250 + 48

OpenStudy (anonymous):

In week # 2....they are starting with 198 bottles, and sell 40% of that...and we add 48 bottles at the end. We dont care to figure out exactly how many bottles they have...the question will ask us to find a mathetical expression for the # of bottles they have each week.

OpenStudy (anonymous):

so far, so good?

OpenStudy (anonymous):

yes, i am understanding it so far :)

OpenStudy (anonymous):

We really dont need to look at week 3...because if we really understand week 1 and week 2, we should be able to answer the question. Now in all the choices...n represents the number of weeks...and the function f(n) represents the total number of bottles they have in stock each week. so let's look at each choice and see which one is true....

OpenStudy (anonymous):

well for some reason c & d look wrong to me. I'm stuck between a and b. I'm thinking the answer is one of those

OpenStudy (anonymous):

Let's study choice A. f(n) = f(n-1) times .4 + 48 So let's put in n = 2...so that means the second week... so if n = 2, we have f(2) = f(1) times .4 + 48 Is this true? Well, that means that in week #2, they have what's in week # 1 times .4 (which is 40%) and then add 48. Is that true?

OpenStudy (anonymous):

The problem with that choice...is that if they sell 40% of the bottles, then they should have 60% or .6 of the first weeks bottles + 48...not .4 or 40% of the water bottles. Does that make sense?

OpenStudy (anonymous):

Yes it does, but c is wrong. right? I'm trying to cancel the wrong answers out first

OpenStudy (anonymous):

So the answer looks like either C or D....because they both have .6...which is 60% ...and we want that. But choice C looks bad as it doesnt start with the 250...agree?

OpenStudy (anonymous):

yes exactly so the answer has to be d !

OpenStudy (anonymous):

So let's see if choice D makes sense. Choice D says: f(n) = 250 - f(n-1) times .6 + 48

OpenStudy (anonymous):

Lets work it out to see if it is choice D.

OpenStudy (anonymous):

Alright :)

OpenStudy (anonymous):

But choice D also doesnt make sense...because look at choice D...it says that in week 2...they will have 250 less 60% of week 1 + 48 bottles.. thats not true...they will have 250 less 40% of week 1 + 48. So it gotta be choice B. Let's look at choice B.

OpenStudy (anonymous):

Nevermind the answer can not be D i can already tell.

OpenStudy (anonymous):

Okay, i got it :)

OpenStudy (anonymous):

Thank you so much! i wrote down the examples and everything so that i can come back to them if i need it :)

OpenStudy (anonymous):

choice B says.... f(n) = 250 - f(n-1) time .4 + 48 which means in week 2...they will have 250 less 40% of week 1 and then add 48 bottles. And that is absolutelt true. In week #2, they will have 250 less 40% of week 1 and then add 48 Do you agree?

OpenStudy (anonymous):

Yes, i do agree!

OpenStudy (anonymous):

Although, I will admit to you that this question is also not worded fully correct...but thats not for now.

OpenStudy (anonymous):

wait.......

OpenStudy (anonymous):

You made this problem a lot easier for me to understand though because you broke it up in to small pieces

OpenStudy (anonymous):

I think we overlooked something... what will they have in week 2?

OpenStudy (anonymous):

wont they have 60% of what they had in week 1 and then add 48?

OpenStudy (anonymous):

in week 2 they will have 250 less 40% of week 1 and then add 48

OpenStudy (anonymous):

Isnt it true that what you wrote is week 1....they start with 250...so in week 1, they will have 250 less 40% + 48

OpenStudy (anonymous):

So when it comes to week #2...they will have 60% of what they had in week 1, and then add 48...true?

OpenStudy (anonymous):

ohhhhhhhhhhh yes!

OpenStudy (anonymous):

So C is the correct choice. Becuase C says that they will have in week #2...60% of week 1 + 48 bottles.

OpenStudy (anonymous):

So in summary...choice C is what is correct. And to prove it...put in n = 5, in choice C.

OpenStudy (anonymous):

Choice C says, n = 5... f(5) = f(4) times 60% + 48 bottles

OpenStudy (anonymous):

and that is true...week # 5 they will have 60% of what they had in week #4 + 48 bottles

OpenStudy (anonymous):

do you agree with me?

OpenStudy (anonymous):

Oh thankgoodness you caught me there before i wrote down the answer :) thankyou so much for the , you honestly made me understand this whole chpter of sequences by breaking it down for me :) Yes i most definitely agree with you!

OpenStudy (anonymous):

OK. Take care and good night.

OpenStudy (anonymous):

goodnight :)

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