Question

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

Answer 1

@rainbow_rocks03

Answer 2

@tkhunny

Answer 3

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?

Answer 4

What do you think the answer is?

Answer 5

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?

Answer 6

i think it is D

Answer 7

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

Answer 8

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

Answer 9

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

Answer 10

@tkhunny

Answer 11

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?

Answer 12

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

Answer 13

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.

Answer 14

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...

Answer 15

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.

Answer 16

can you help with another?

Answer 17

Only one way to find out :-)

Answer 18

What is the final balance for the investment?

$20,000 for 3 years at 5% compounded annually



$ ___________

Answer 19

do you know the difference between compound and simple interest?

Answer 20

no...

Answer 21

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?

Answer 22

yes that makes since

Answer 23

so how do i find the answer to this question?

Answer 24

Now compound interest is different. Notice that the amount of interest added each period was the same with simple interest — 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

Answer 25

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

Answer 26

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?

Answer 27

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

Answer 28

im confused

Answer 29

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.

Answer 30

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

Answer 31

on the question

Answer 32

for*

Answer 33

there are 3 periods...

now the interest rate is 5%, how do you express that as a decimal?

Answer 34

0.05

Answer 35

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

Answer 36

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 = \(2^3\)

Answer 37

im confused

Answer 38

FV=PV(1+i)^n

Answer 39

like that?

Answer 40

@whpalmer4

Answer 41

yes, but can you put the numbers in?

Answer 42

what is FV and PV

Answer 43

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.

Answer 44

FV=20,000 and PV=3?

Answer 45

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

Answer 46

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
\[FV = 20000(1+0.05)(1+0.05)(1+0.05) = 20000*(1.05)(1.05)(1.05)\]

Answer 47

is the answer 23152.5

Answer 48

I believe it is, yes :-)