Identify the independent and dependent variables.
Larry is conducting an experiment to see how many inches of snowfall occur each hour during the day.
A.
Independent: day of the week Dependent: inches of snowfall
B.
Independent: hours in a day Dependent: inches of snowfall
C.
Independent: time of day Dependent: inches of snowfall
D.
Independent: inches of snowfall Dependent: time of day

- anonymous

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- anonymous

@rainbow_rocks03

- anonymous

@tkhunny

- whpalmer4

Does the day of the week depend on the amount of snow, or does the amount of snow depend on which day of the week it is?

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## More answers

- rainbow_rocks03

What do you think the answer is?

- whpalmer4

Or, asked a different way, if you were going to graph this, with amount of snow on one axis, and the day of the week the other, would you make the day of the week be the x-axis, or the amount of snow?

- anonymous

i think it is D

- whpalmer4

Let's try to understand the concept first, and worry about which answer it is second...

- anonymous

well @rainbow_rocks03 asked me what i think it is and so i said D

- rainbow_rocks03

I will ask a friend to help you cause I can't sorry

- rainbow_rocks03

@tkhunny

- whpalmer4

Okay, why do you think that?
Isn't a key to answering this going to be understanding how to identify the independent variable and the dependent variable?

- tkhunny

Which can be deliberately selected and which will be unknown until it is measured?

- anonymous

i thought is was D because you can't control the amount of snow that comes but you can control the time of day you do it at.

- whpalmer4

so the time of day is the independent variable...and the snowfall amount is the dependent variable because it depends on the time of day...

- whpalmer4

or as tkhunny put it, you can select the time of day, so it is the independent variable, and you then measure the snowfall, so it is the dependent variable.

- anonymous

can you help with another?

- whpalmer4

Only one way to find out :-)

- anonymous

What is the final balance for the investment?
$20,000 for 3 years at 5% compounded annually
$ ___________

- whpalmer4

do you know the difference between compound and simple interest?

- anonymous

no...

- whpalmer4

okay, that's a pretty important thing to understand!
Simple interest is computed by taking the principal value (the amount you borrowed or invested), and multiplying it by an interest rate. That gives you the interest for one period. If there are multiple periods, you multiply the interest by the number of periods to get the total interest.
An example:
I lend you $100 for a year, and charge you 5% interest per year. At the end of 1 year, you owe me the original $100, plus 5% interest on $100, which is 0.05*$100 = $5, for a grand total of $105.
If we had an agreement that you could borrow the money for 3 years, still at 5% simple interest each year, each year, the balance would go up by 5% of $100. At the end of 3 years, you would owe me
$100 + $5 + $5 + $5 = $115
Does that make sense?

- anonymous

yes that makes since

- anonymous

so how do i find the answer to this question?

- whpalmer4

Now compound interest is different. Notice that the amount of interest added each period was the same with simple interest â€” just the percentage times the principal value.
With compound interest, the interest is computed by multiplying the entire balance by the percentage. For the first period, the result is the same. For the second period, instead of multiplying the principal balance by the interest rate, we multiply the principal balance + all of the interest owed up to that point.
$100 + 5%*$100 = $100+$5 = $105
$105 + 5%*$105 = $105 + $5.25 = $110.25
$110.25 + 5%*$110.25 = $110.25 + $5.51 = $115.76
compare that with simple interest:
$100 + 5%*$100 = $100+$5 = $105
$105 + 5%*$100 = $105+$5 = $110
$110 + 5%*$100 = $110+$5 = $115

- whpalmer4

If the interest rate is large, or there are a large number of periods, or both, the compound interest version turns into a much larger number than the simple interest version!
For example, if we said 10% interest, and 7 years:
$100 turns into $100+10%*$100*7 = $100 + $70 = $170
Compound interest, same interest rate, same number of years:
$100 turns into $100(1.1)^7 = $194.87

- whpalmer4

The formula for compound interest is
\[FV = PV(1+i)^n\]where \(FV\) is the future value, \(PV\) is the present value, \(i\) is the interest rate, expressed as a decimal, and \(n\) is the number of periods.
Here for your problem, we have\[PV=$20,000\]and we want to find \(FV\) after 3 years at 5%, compounded annually.
How many periods do we have, and what value do we use for \(i\) in that formula?

- anonymous

um..... what do you mean by periods?

- anonymous

im confused

- whpalmer4

periods are the chunks of time over which the compounding is done. If you are compounding annually, the length of a compounding period is 1 year. If you are compounding monthly, the length of a compounding period is 1 month.

- anonymous

ok, so we are doing compound annually.... so the period is 3 years

- anonymous

on the question

- anonymous

for*

- whpalmer4

there are 3 periods...
now the interest rate is 5%, how do you express that as a decimal?

- anonymous

0.05

- whpalmer4

Correct. So you can write out the formula, substituting all the known values?

- whpalmer4

The formula uses \(n\) as an exponent, and you probably don't know how to typeset things, so just put ^ before the exponent, like 2^3 = \(2^3\)

- anonymous

im confused

- anonymous

FV=PV(1+i)^n

- anonymous

like that?

- anonymous

@whpalmer4

- whpalmer4

yes, but can you put the numbers in?

- anonymous

what is FV and PV

- whpalmer4

PV is the amount of money at the start, and FV is the amount in the future. The final balance in the problem is the FV.

- anonymous

FV=20,000 and PV=3?

- anonymous

20,000=3(1+i)^n

- whpalmer4

no, FV is what we are trying to find. PV is $20,000, i = 0.05, n = 3
so the FV = 20000(1+0.05)^3 which is the same as
\[FV = 20000(1+0.05)(1+0.05)(1+0.05) = 20000*(1.05)(1.05)(1.05)\]

- anonymous

is the answer 23152.5

- whpalmer4

I believe it is, yes :-)

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