Please help me (NO DIRECT ANSWERS) :)
I WILL MEDAL/FAN

- anonymous

Please help me (NO DIRECT ANSWERS) :)
I WILL MEDAL/FAN

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- anonymous

Belinda wants to invest $1000. The table below shows the value of her investment under two different options for three different years:
Number of years 1 2 3
Option 1 (amount in dollars) 1300 1690 2197
Option 2 (amount in dollars) 1300 1600 1900
Part A: What type of function, linear or exponential, can be used to describe the value of the investment after a fixed number of years using option 1 and option 2? Explain your answer. (2 points)
Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years. (4 points)
Part C: Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option. (4 points)

- anonymous

@saseal last one :)

- anonymous

lemme study this wall of text

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## More answers

- anonymous

okay dookie

- anonymous

Part A is asking about linear and exponential function, you know the different between em right?

- anonymous

Yes ma'am/sir

- anonymous

im doge xD

- anonymous

so a guyyy??? Like I am really slow btw

- anonymous

you can prolly guess which one is a linear function and exponential just by looking

- anonymous

maybeee???

- anonymous

i can but i dont know about you

- anonymous

option one is exponential and option 2 is linear

- anonymous

possibly
OS makes me feel really stupid

- anonymous

you are correct

- anonymous

but for the explanation part

- anonymous

option two is linear because it increases by a fixed amount?

- anonymous

its describing the difference between this 2 functions. btw “Everybody is a genius. But if you judge a fish by its ability to climb a tree, it will live its whole life believing that it is stupid.” - Albert Einstein

- anonymous

yea

- anonymous

okay so "option two is linear because it increases by a fixed amount"

- anonymous

yea

- anonymous

I am not sure about option one though

- anonymous

when you did the last question, exponential increase by what factor?

- anonymous

the f(x) of your last question

- anonymous

3%

- anonymous

its a power right?

- anonymous

0.69*1.03^x

- anonymous

its a compounding 3%

- anonymous

yes...but this question doesn't have an equation.

- anonymous

yea that f(x) is an exponential equation just like option 1

- anonymous

whatt?

- anonymous

they behave the same way

- anonymous

like this on the graph|dw:1438877568681:dw|

- anonymous

they have different flavors but they increase to a very steep gradient in the end

- anonymous

increase or decrease depends on the function

- anonymous

they dont behave like a linear function which looks like this on the graph|dw:1438877675414:dw|

- anonymous

okayy sooo...

- anonymous

option b has a quantity growth proportional to its current value

- anonymous

thats what makes it exponential

- anonymous

option a you mean?

- anonymous

yea

- anonymous

Part B now?

- anonymous

Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years.

- anonymous

option 2 first: its y=mx+b
option 1: you want me to hand you compound interest formula?

- anonymous

what? I know y=mx+b. But how does that apply to this? and yes please

- anonymous

y=mx+b
b is your y-intercept where its year 0 which is 1000. now from there what is the rate of change of the $$$ per year? that will be your m

- anonymous

okay. Help?

- anonymous

compound interest formula\[A=P(1+\frac{ r }{ 100 })^n\]

- anonymous

A=amount accumulated
P=principal amount
r=interest rate
n=years

- anonymous

yes I know that we were taught this: f(x)=p(1+r)^x
where r was the rate in decimal form, p was principle and x was x

- anonymous

y=mx+1000
1000 is your principal

- anonymous

okay

- anonymous

now lets find your m with 2 points

- anonymous

ok, what about 1 and 0

- anonymous

0 is year 0, whats your $ at year 0?

- anonymous

for option B?its 1000

- anonymous

now year 1 of option b?

- anonymous

1300

- anonymous

now you have your 2 points (0,1000) and (1,1300)

- anonymous

you can find your slope from here

- anonymous

\[m=\frac{ y_2-y_1 }{ x_2-x_1 }\]

- anonymous

1300-1000/1-0

- anonymous

yes

- anonymous

300/1 or 300

- anonymous

nvm ill show you the simple interest formula so you dont get confused

- anonymous

okay?

- anonymous

\[I=P \times R \times T\]

- anonymous

OKOKOKOk wut?

- anonymous

interest rate is \[\frac{ 1300-1000 }{ 1000 } \times 100\]
I = interest created
P = principal
R = interest rate
T = time

- anonymous

300/1000*100=30

- anonymous

yup

- anonymous

we are still on part B?

- anonymous

right?

- anonymous

yes

- anonymous

okay. What was that the answer to? 30

- anonymous

now we are support to create function

- anonymous

okay so f(x)=300

- anonymous

lol

- anonymous

we piece the part of the simple interest formula + principal to get the answer

- anonymous

like this f(x)=x+(P*R*T)

- anonymous

ok

- anonymous

oops its f(x)=1000+(1000*R*x)

- anonymous

since x is time which is the only thing that changes

- anonymous

test this function see if it works

- anonymous

So the answer to part B for Option 2<< or 1 am not sure is f(x)=1000+(1000*R*x)

- anonymous

lets see...\[f(1)=1000+(1000*0.3*1)=1300\]\[f(2)=1000+(1000*0.3*2)=1600\]

- anonymous

thats good for your part b option 2

- anonymous

for option 1 its the compound interest formula, you can find your interest rate like this\[\frac{ 1300-1000 }{ 1000 } \times 100\]

- anonymous

\[f(x)=1000(1.3)^x\]

- anonymous

"f(1)=1000+(1000∗0.3∗1)=1300
f(2)=1000+(1000∗0.3∗2)=1600" for option b?

- anonymous

nah its \[f(x)=1000+(1000*0.3*x)\]you can simplify it further if you like to

- anonymous

well its an essay q, I do not know what its asking for, but I gave the specific question

- anonymous

they say write function, you cant write an essay on that

- anonymous

not literal essay, I mean its not graded by the computer, its by the teacher, so I am not sure what specifically the answer is, since ther are no multiple choice.

- anonymous

they are asking you to craft a function that whenever you put in a year, it will churn out something that tells you the $ you get when you put your $ in for that amount of year

- anonymous

okay moving on. Option A?

- anonymous

scroll up abit

- anonymous

okay. Part C?

- anonymous

Belinda wants to invest in an option that would help to increase her investment value by the greatest amount in 20 years. Will there be any significant difference in the value of Belinda's investment after 20 years if she uses option 2 over option 1? Explain your answer, and show the investment value after 20 years for each option.

- anonymous

now plug in 20 into both functions and see the difference

- anonymous

where is the n in the function for option 1?
f(x)=1000(1.3)x
WOAH WOAH WOAH JUST TO GET THIS ALL CLEAR,
OPTION 2: f(x)=1000+(1000*0.3*n)
OPTION 1:f(x)=1000(1.3)x

- anonymous

yea

- anonymous

Option 1:\[f(x)=1000(1.3)^x\]Option 2:\[f(x)=1000+(1000*0.3*x)\]

- anonymous

OKAY so next, we fill in 20
f(x)=1000*190.049637749

- anonymous

- anonymous

yea no problem

- anonymous

now compare that to option 2

- anonymous

f(x)=1000+(1000∗0.3∗20)
7000 and

- anonymous

190049.637749 and 7000

- anonymous

whats 190049.637749-7000

- anonymous

183049.638

- anonymous

now you got your numbers go explain it

- anonymous

do you think 180349.638 is a signifcant difference?

- anonymous

yeahhh

- anonymous

thanks for the help :)

- anonymous

yw

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