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Guest:
suppose that the rate of inflation for the last four years was 3.9% per year. if a home costs 125,000 today, how much would it have cost four years ago?

You just use the compound interest formula

S = P(1+r) ⁿ

S is future value - which is 125,000 (Because the question is looking back, it wants you to work out an earlier value)
P is present value (or initial value) which is what you are trying to find.
r is the rate per compounding period. In this case the compounding period is in years. r = 0.039
n is the number of compounding periods which is 4

Try doing it yourself now.

MelodyFeb 4, 2014

+118725

mathy6161:
:D What is 5x>64

simple, just divide both sides by 5

You only need to turn the sign around if
1 You multiply or divide by a negative number
2 You swap sides
3 you take the reciprocal of both sides (turn both sides upside down)

MelodyFeb 4, 2014

+118725

student789:
cscx/cotx+tanx=cosx

Hi Student789

co sec = 1/ sin

co t = 1/ tan

** The first letter of the most familiar ratio matches the 3'rd letter of the less used ratio,

Lets see,

1/sinx divided by 1/tanx + tanx = cosx

1/sinx multiplied by tanx + tanx = cosx

NOW, tanx =sinx/cosx

1/sinx times sinx/cosx + sinx/cosx = cosx

1/cosx + sinx/cosx = cosx

(1+sinx) / cosx = cosx

1+sinx = cos ²x

1+sinx = 1-sin ²x

sin ²x + sinx = 0

sinx(sinx + 1) = 0

sinx = 0 or sinx = -1

Can you finish it ?

MelodyFeb 4, 2014

+135

Melody:

e^ln(2x) = e^-4/7

2x = -4/7

Oops!
I think you dropped an "e".

Hey SelinaMarie!

I see you came up with a couple of good answers!

I like SerenaFeb 4, 2014

Feb 3, 2014

+118725

Guest:
how do multiply negatives

If you just want to multiply negative (and positive) numbers its is simple and it works exactly the same for division as well.

If the signs are the same the answer is positive.
If the signs are different the answer is negative.

It's adding and subtracting that is more complicated.

MelodyFeb 3, 2014

+118725

SelinaMarie:
-7* (natural logarithm) ln(2x)=4
could someone show me how to work this out?

Hi SelinaMarie

It is nice to see you again.
I know that you answer questions as well as ask them and I really appreciate this.
I do an end of day wrap each night. If you read it already, that's great, if not maybe you would like to sometimes.
I know you are not a member yet and I would really like you to join up.
I've given a list of benefits in one of my recent nightly wraps if you would like to take a look.

Now to your question,
-7* (natural logarithm) ln(2x)=4

-7ln(2x) = 4

ln(2x) = -4/7

e ^ln(2x) = e ^-4/7

2x = e ^-4/7 Edit: Sorry, I like Serena was right, i did drop an e. sorry

etc

I got the exponents up in the air by using the 'sup' button that is located above the icons.

e and ln cancel each other out, much like + and -
so

e ^ln6 = 6

10 ^log4 = 4

ln e ⁷ = 7lne = 7*1 = 7

log 10 ¹² = 12log10 = 12*1 = 12 ( base 10 of course)

Any questions? Just ask.

MelodyFeb 3, 2014

+6252

a mole? like this? http://24.media.tumblr.com/tumblr_m8jlf21t7V1qghjizo1_250.jpg ?

Assuming you mean a million you just divide 1,000,000 by 100

1000000/100 = 10000

this would be 100 of those bundles you see in briefcases in spy flicks.

RomFeb 3, 2014

+6252

Quote:
-7* (natural logarithm) ln(2x)=4

-7 ln(2x) = 4

ln(2x) = -4/7

e ^ln(2x) = e ^-4/7

2x = e ^-4/7

x = 1/2 e ^-4/7

RomFeb 3, 2014

negative what?? -2*-2=4?...negative radicals? negative exponents???

GuestFeb 3, 2014

+6252

Compound interest just takes a given annual rate, divides it by some number of periods per year K, and applies that new interest rate K times a year.

The formula for the future value, given rate r, over N years, compounded K times a year is

FV = PV*(1+r/K) ^KN

To compare, let's say you have 5% annual interest

Compounded annually you would have, over say 30 years

FV = PV*(1+0.05) ³⁰

FV/PV = 4.322

Compounded quarterly you would have

FV = PV*(1+0.05/4) ^4*30 = PV*(1+0.0125) ¹²⁰

FV/PV = 4.440

For equal rates and years and present values compounding yields a higher future value.

Now how does this relate to exponential growth?

If you recall exponential growth is described by

f(t) = f0*e ^g*t where f0 is the initial value of f and g describes the growth or decay rate. Positive g is growth, negative g is decay. A higher value of g leads to faster growth or decay.

now rewrite your compound interest formula as a function of t years

FV(t) = PV*(1+r/K) ^K*t

remembering that b ⁿ = e ^n*log(b) we get

FV(t) = PV*e ^{log(1+r/K)*K*t}

i.e. FV(t) is exponential growth with

f0 = PV
g = log(1+r/K)*K

RomFeb 3, 2014

the fourth root of 4096?
or
the square root of (4096)^4 ?

GuestFeb 3, 2014

3/3^-4
because the three on the bottom is to the negative power of four you should make the exponent positive by moving to the numerator so...
3*3^4 which is 3*81= 243

GuestFeb 3, 2014

+6252

262144 = 2 ¹⁸

RomFeb 3, 2014

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Quote:

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Girl...Just girl:
What does -7/3n= -42 equal?

I'm sorry, I just suck at algebra.

Plus it's not cheating if I tried to solve it, and I can't seem to get the answer right. I even asked my family member for help and they couldn't help me at (neither did they try to help me).

PLEASE HELP!

GuestFeb 3, 2014

yes

GuestFeb 3, 2014

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