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

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

Mathematics
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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)
@saseal last one :)
lemme study this wall of text

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Other answers:

okay dookie
Part A is asking about linear and exponential function, you know the different between em right?
Yes ma'am/sir
im doge xD
so a guyyy??? Like I am really slow btw
you can prolly guess which one is a linear function and exponential just by looking
maybeee???
i can but i dont know about you
option one is exponential and option 2 is linear
possibly OS makes me feel really stupid
you are correct
but for the explanation part
option two is linear because it increases by a fixed amount?
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
yea
okay so "option two is linear because it increases by a fixed amount"
yea
I am not sure about option one though
when you did the last question, exponential increase by what factor?
the f(x) of your last question
3%
its a power right?
0.69*1.03^x
its a compounding 3%
yes...but this question doesn't have an equation.
yea that f(x) is an exponential equation just like option 1
whatt?
they behave the same way
like this on the graph|dw:1438877568681:dw|
they have different flavors but they increase to a very steep gradient in the end
increase or decrease depends on the function
they dont behave like a linear function which looks like this on the graph|dw:1438877675414:dw|
okayy sooo...
option b has a quantity growth proportional to its current value
thats what makes it exponential
option a you mean?
yea
Part B now?
Part B: Write one function for each option to describe the value of the investment f(n), in dollars, after n years.
option 2 first: its y=mx+b option 1: you want me to hand you compound interest formula?
what? I know y=mx+b. But how does that apply to this? and yes please
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
okay. Help?
compound interest formula\[A=P(1+\frac{ r }{ 100 })^n\]
A=amount accumulated P=principal amount r=interest rate n=years
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
y=mx+1000 1000 is your principal
okay
now lets find your m with 2 points
ok, what about 1 and 0
0 is year 0, whats your $ at year 0?
for option B?its 1000
now year 1 of option b?
1300
now you have your 2 points (0,1000) and (1,1300)
you can find your slope from here
\[m=\frac{ y_2-y_1 }{ x_2-x_1 }\]
1300-1000/1-0
yes
300/1 or 300
nvm ill show you the simple interest formula so you dont get confused
okay?
\[I=P \times R \times T\]
OKOKOKOk wut?
interest rate is \[\frac{ 1300-1000 }{ 1000 } \times 100\] I = interest created P = principal R = interest rate T = time
300/1000*100=30
yup
we are still on part B?
right?
yes
okay. What was that the answer to? 30
now we are support to create function
okay so f(x)=300
lol
we piece the part of the simple interest formula + principal to get the answer
like this f(x)=x+(P*R*T)
ok
oops its f(x)=1000+(1000*R*x)
since x is time which is the only thing that changes
test this function see if it works
So the answer to part B for Option 2<< or 1 am not sure is f(x)=1000+(1000*R*x)
lets see...\[f(1)=1000+(1000*0.3*1)=1300\]\[f(2)=1000+(1000*0.3*2)=1600\]
thats good for your part b option 2
for option 1 its the compound interest formula, you can find your interest rate like this\[\frac{ 1300-1000 }{ 1000 } \times 100\]
\[f(x)=1000(1.3)^x\]
"f(1)=1000+(1000∗0.3∗1)=1300 f(2)=1000+(1000∗0.3∗2)=1600" for option b?
nah its \[f(x)=1000+(1000*0.3*x)\]you can simplify it further if you like to
well its an essay q, I do not know what its asking for, but I gave the specific question
they say write function, you cant write an essay on that
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.
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
okay moving on. Option A?
scroll up abit
okay. 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.
now plug in 20 into both functions and see the difference
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
yea
Option 1:\[f(x)=1000(1.3)^x\]Option 2:\[f(x)=1000+(1000*0.3*x)\]
OKAY so next, we fill in 20 f(x)=1000*190.049637749
yea no problem
now compare that to option 2
f(x)=1000+(1000∗0.3∗20) 7000 and
190049.637749 and 7000
whats 190049.637749-7000
183049.638
now you got your numbers go explain it
do you think 180349.638 is a signifcant difference?
yeahhh
thanks for the help :)
yw

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