Question

@ajaylounsber Jennifer has been saving for college for 57 months. The first month, she saved $11. She was able to save more money each month than the month before. She ended up saving $19,779.00. How much more did she save each month?

Answer 1

theres missing info

Answer 2

$11
$11.50
$12
$12.50

Answer 3

tell me more like how much needs to save up to ok?

Answer 4

That's all they gave me.

Answer 5

jeremyggg take it awy

Answer 6

Did you type it exactly word for word? It does seem to be worded strange.

Answer 7

i know

Answer 8

yes they are word for word

Answer 9

Im thinking it's a set amount more each month. 11 22 33 44 55 type thing ajay

Answer 10

19,768

Answer 11

so if it is a set so how do i know how much... to be honest the question is so weird to me

Answer 12

the answer i typed in is right

Answer 13

Which class is this for? There could be a few ways to solve this

Answer 14

Algebra 2

Answer 15

im taking it online

Answer 16

simple subtrsction problem

Answer 17

lily have you learned about factorials and summations in this class? does what i showed you look familar?

Answer 18

$11
$11.50
$12
$12.50
it has to be one of them

Answer 19

Yes it does.

Answer 20

add to 11 57 times

Answer 21

one of those answers

Answer 22

yea

Answer 23

yes

Answer 24

wording is confusing because if she was able to save more money then the month before, how can what she saved be a constant rate

Answer 25

She saves an exact amount more than the previous. like a series or summation.
11 + (11+x) + (11+ 2x)+(11+3x) ....(11+57x) = 19779
do you know how to set this up in a summation lilystacy? maybe you can give it a try?

Answer 26

No i do not know how.....

Answer 27

Ok well, when you have a summation (this symbol)\[\sum_{k}^{n}\] you add these values over and over where k is your starting point and n is the end point. we know the first month needs to be 11 + 0 and each additional month is adding 1 to the multiplier of x. sounds confusing i know. but this is what we are doing.
month 1: 11 + 0x
month 2: 11+ 1x (because x is the amount she saves more than last month)
month 3: (11+ 1x) + x (11 +1x is the amount she saved last month)
month 4 (11+2x)+x and so on. we have our pattern!

so we want to start at 0 so that we can get 11. if we start at zero we need to go to 56 to make a total of 57 months.

\[\sum_{k=0}^{56} 11 +kx = 19779\]
does your calculator let you type this to solve for x?

Answer 28

i have my calculator right now but i do not know how to plug them in

Answer 29

Hmm, i am not sure of your calculator. I know a website I use called wolframalpha.com where i sometimes checked my answers when i forgot my calculator. The answer I got when plugging this in is 12.

Answer 30

yayyyy Jeremyggg it's right you did it

Answer 31

and this is what i handtyped in the website.
summation k =0 to 56 (11 + xk) = 19779 those exact words!

Answer 32

There is a hand way of doing this. I'm trying to remember the steps so maybe you can do these without a calculator! do you think you need these steps?

Answer 33

Can you help me again please given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.
n an
-4
20
-100
1
2
3

Answer 34

an = −5(−4)n − 1 where n ≥ 1

an = −4(−5)n − 1 where n ≥ 1

an = −4(5)n − 1 where n ≥ −4

an = 5(−4)n − 1 where n ≥ −4

Answer 35

ooh i used to like these i think. ok let's see...

Answer 36

There is a formula we need. something along the lines of \[a _{n} = a _{1}*r ^{n-1}\]
does this one sound familiar or right?

Answer 37

yes

Answer 38

where r is the ratio between each number

Answer 39

ok we have a1 already right?
now let's figure out r!
(let me know if/when you get lost)

Answer 40

I'm here

Answer 41

ok, just to make sure you are keeping up, let me know what a1 and r equal if you know em! they are simple, but this stuff can get confusing really fast.

Answer 42

This is the first time i'm seeing those thing and they gave me a lesson i don't even know what they are saying,,,,

Answer 43

Jeremyggg are you there

Answer 44

yes sorry!

Answer 45

alright well, let's teach how this works.
n an
1 -4
2 20
3 -100

this is saying that we have this series (i like to think of em as patterns or puzzles)
where a1 = -4 a2= 20 and a3=-100
r is going to be a ratio between them, and being a geometric sequence, this ratio will be constant.
what do you do to a1 to make a2=20 and what do you do to a2 to make a3= -100? this is your r!

Answer 46

with this info we have most of our answer already!
an = a1* r^n-1

or...
an= -4(r)^n-1

Answer 47

that's the answer

Answer 48

Yes, but what is r?

Answer 49

remember r as the word ratio!

Answer 50

is it 4

Answer 51

i guess it might help that i explain what we are doing. we are coming up with an equation where if i wanted to know what a10 was, i could just plug 10 into the equation that we created. like for example, what we solved earlier! i wanna know the 57th month, i just plug 57 into the equation and im done!

Answer 52

no no. let us review the table again.
a1= -4
a2 = 20
a3= -100
r = the ratio between each of these numbers. there is something that happens to a1 that makes it equal a2. the exact same thing happens to a2 to make it a3. and if there was an a4, the exact same thing would happen to 3 to make a4.

Answer 53

So 4 is wrong then we only have 1

Answer 54

the ratio is -5!
-4 * -5 = 20
20*-5 = 100! so r = -5

Answer 55

to go from a1 to a2 we must multiply by -5.
to go from a2 to a3 we must multiply by -5.
this is what i am meaning by ratio

Answer 56

It can't be -5 remember we have
an = −5(−4)n − 1 where n ≥ 1

an = −4(−5)n − 1 where n ≥ 1

an = −4(5)n − 1 where n ≥ −4

an = 5(−4)n − 1 where n ≥ −4
that's are the options they gave me

Answer 57

yes. and remember the equation i gave you?
an = a1*r^n-1

Answer 58

a1 = -4 based on the chart.
r = -5 based on what we solved for the ratio!
an = a1*r^n-1 orrrrr....
an = -4(-5)^n-1

Answer 59

B IS THE ANSWER

Answer 60

yes! The bounds can be a bit tricky to explain until you grasp what is going on with this one a bit better

Answer 61

erm... restrictions on domain, not bounds

Answer 62

Thank you so much

Answer 63

No problem! If you need any more help just send me a message! And if you need a better explaining than this, because this was one of my worst attempts at teaching, also let me know!

Answer 64

Alright right now i'm looking at what i need help with if i find some i let you know.

Answer 65

just now finish it wow

Answer 66

ooh we did 2 of them ajay!

Answer 67

oh ok but dang

Answer 68

next time don't use one with some one tagged in the question it get's anoying

Answer 69

you left us

Answer 70

I said for him to take it away

Answer 71

Oh Ok

Answer 72

A study of college freshmen found that students who watched TV for more than one hour each night gained 15 pounds in the first semester, compared to those who watched less than one hour. They concluded that there is an association between watching TV and weight gain in college freshmen. Which study design did they most likely use?

Answer 73

Answers
They most likely used an experiment with students randomly assigned to watch more than one hour or less than one hour of TV each night.

They most likely used an experiment with students randomly assigned to groups based on how much weight they gained.

They most likely used an observational study asking students to keep track of their TV habits and weight.

They most likely used an observational study asking students to keep track of their workout regimen and weight.

Answer 74

Jeremyggg are you there i have five more 3 of them i have the answers and i don't know 2 of them could you help me please.

Answer 75

damn

Answer 76

use diffrent onr please