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I think this is how you want to to solve for K:

y=yo.e^(K5700), now you set y to the left 1/2y and you get

1/2y=yo.e^(K5700) divide both sides by y

1/2=e^(K5700) take the natural log of both sides

-0.693147=K5700 and

K=-.693147/5700

K=-1.215 X 10^-4 and that's what you are trying to get.

I have plugged in the numbers but not sure what to do next. y=100e^5700K

Since you have used 100 units of Carbon-14, and you have 1 half-life, it therefore follows that "y" to the left-hand side will be 50 units. But instead of using 5700 as a power of e, I think you should use 1, because 5700=1 half-life. using 5700 as a power of e, you are going to get an extremely large number or an extremely small number, being the reciprocal of 5700. Do you see it? Then just solve for the constant K as follows:

Solve for K:
50 = 100 e^1 K

50 = 100 e K is equivalent to 100 e K = 50:
100 e K = 50

Divide both sides by 100 e:
Answer: | K = 1/(2e)

P.S. There is a much simpler way of finding out the amount of a radioactive material left over after n half-lives: Since you have 1 half-life in this example, then it goes like this:

2^-n X 100=2^-1 X 100=1/2 X 100=50% of the original material left after 1 half-life.

NeedSupply: I forgot to mention to you that I was suspicious of their quoting two discounts rates of "30% and 10%".  They could very well mean that the discount isn't 30 + 10=40%, which is what I assumed, but 30%+10% of 30%, which would be a discount of 33% instead of 40%. If you have seen before, which I haven't, then it should be clear to you what they mean. If it is 33%, then that means you have to r-do all the calculations. But that shouldn't be a big deal, since it will take you 10-15 minutes to re-calculate all the numbers. You should have it clarified one way or another. Good luck to you.

This type of equation has an infinite number of solutions, such as: x=4 and y=34 or x=67 and y=7.....etc.

Answer: The man was a fisherman and was telling somebody on the phone about the large fish he caught. When he used his hands to gesture how big the fish was he hit the glass breaking it and cutting himself.

Sorry, I cheated. 

He got shot from outside while he talked on the phone.

The bucket and stick were his. He was using them to collect and carry nuts and left them outside while he made the call.  The nut farmer was very cross. That is why he shot the theif.

Central Ski and Cycle purchased 50 pairs of ski boots for $350 per pair less 30% and 10%. The regular rate of markup on selling price of the boots is 50%. The store’s overhead is 25% of the selling price. During a January clearance sale, the price was reduced to $325 per pair.  What is the rate of markdown and what was the profit or loss on each pair of boots at the sale price? Answer to the nearest cent.

Any help with calculations would be greatly appreciated , thanks

This is a bit tricky in that it deals with "markups" and " markdowns". Let us see what we can do:

Since they got discounts of 30% and 10% on each pair of $350 boots, the net cost to them would be:

$350.00 - 30% - 10%=$220.50 net cost per pair of boots to the company. But, the company, presumably, intends to sell them at the advertised price of $350 per pair.

So, if they have a sale in January at $325 per pair, the rate of markdown from $350 to $325 would be 7.14%.

Since the markup is 50% of the sale price, then each pair is sold in January for $325 X 1.50=$487.50.

But, the company has "an overhead cost of 25% of the selling price", which means, I think!, that 25% has to come off the selling price of $487.50. If that's right, then $487.50 - 25%=$365.63 net sale price per 1 pair of ski boots.

Since it cost the company $220.50 net per 1 pair of boots, and it sold it for $365.63, then the net profit per 1 pair of ski boots would be:$365.63 - 220.50=$145.13

I think it is right, but I'm no expert in "retail sales"!. See if this makes sense to you!. Good luck.

4A = A( 1 + .08/2)^(2n)       divide both sides by A

4 = ( 1 + .08/2)^(2n)           take the log of both sides

log [4]   =  log (1.04)^(2n)     and we can wrtie

log [4]  =  (2n) log (1.04)      divide both sides by 2log(1.04)

log [4]  / [2log(1.04)]  = n   =   about 17.67 years  ≈  17 + 2/3   years

Thanks guest,

I like your method better than my one. 

1+99=100

3+97=100

5+95=100

7+93=100...

Guest
12 mins ago     

Can you do 1 + 3 + 5 + 7 + ... + 99 in your head And how

There is a formula to solve this.

SUM= n/2(a+L)

a is the first number =1

L is the last number =99

n is the number of numbers = 50

So

Sum=25×100=2500

Sorry....I initially misread the question.....

There will be 25 pairs of numbers that will sum to 100, thusly.....

[99 + 1], [ 97 + 3], [ 95 + 5], etc.

So.....the sum is just 2500

Rounded to the nearest quarter year, how long will it take an investment to quadruple if it earns 8% compounded semi-annually?

Any help would be greatly appreciated with calculations.

Thanks

This is very simple and easy problem to solve. He is basically asking: How long would it take for $1 to become $4 @8% S.A.

The first thing you should do is to convert 8% from S.A. compound to quarterly compound, which comes to 7.92% comp. quarterly. Then you would solve for n, or number of periods. If you do it right, you should get: 70.69 quarters, or rounded to the nearest quarter=71 quarters. or 70.69/4=17 years and 3 quarters(rounded to neatest quarter).

The formula you use is the same PV formula that you know. The only difficulty you might have is solving for n. You have to use Logs to do that.

Thanks, everyone......!!!!!

BTW.......just so I don't forget........HAPPY [EARLY] BIRTHDAY wishes, DS.....!!!!!!!

Ramon wishes to replace payments of $900 due today and $500 due in 22 months by a single equivalent payment 18 months from now. If money is worth 4.8% compounded monthly, what should that payment be?  Interim calculations to 3 decimals, final answer rounded to the nearest cent.

Any help with calculations would be greatly appreciated.

First, you have to find the PV of $500 due in 22 months, which comes to:

$457.961. To this you have to add $900 due today, so you have:

$457.961 + $900=$1,357.961 PV of the the two payments. Since Ramon wants to replace these 2 payments by a single payment due in 18 months. So, you have to project this amount 18 months from now at 4.8%, which comes to $1,459.13. This is the single payments replacing the other two of $500 and $900.

The formulae you use are the two common one of PV and FV, which you already have.

Arcelor Mittal Dofasco can buy iron ore pellets from Minnesota at US$130 per short ton (2000 pounds) or from Labrador at C$175 per metric tonne (1000 kg). Which source is more expensive and by how much in C$ per metric tonne? (1 pound = 0.4536 kg, C$1.1400 = US$1.00) Weight and currency calculations should be to 4 decimal places; final answer rounded to the nearest cent.

Any help would be greatly appreciated thanks with calculations

First, you have to make both the currencies and the kilo and pounds equivalent: So, we have:

$130 US X 1.14=$148.2 Canadian, then we also have:

2,000lb X .4536=907.2 Kilos. Now you can compare properly:

907.2 / 148.2=$6.12 Canadian dollars per Kilo from Minnesota.

1,000 / 175   =$5.71 Canadian dollars per Kilo from Labrador.

So, obviously the purchase from Minnesota is more expensive by:

$6.12 - $5.71=$.41 or 41 cents Canadian per Kilo.

P.S. Please use the same reasoning BUT, check my calculations!.

Karim works in a retail computer store. He receives a weekly base salary of $400 plus a commission of 3% of sales exceeding his quota of $25,000 per week. What are his total sales for a week in which he earns $730.38?  Answer to the nearest cent.

Any help would be appreciated, thanks, with calculations

$730.38 - $400.00=$330.38 This is karim's commission in a week.

$330.38/3%=$11,012.67 This is the total sales on which he earned 3% commission, but he has a quota of $25,000 in sales before he gets any commission. Therefore, his total sales must be:

$25,000 + $11,012.67=$36,012.67 for 1 week.

NO!. An annuity with fixed patments, its PV or purchase price would DECREASE with increase in interest rates: Example: $100,000 annuity at 4% interest that would pay you fixed annual payment of $7,358.18 for 20 years. If interest rates went up to 5% and the payments remained exactly the same for 20 years, the PV or the purchase price would be: $91,699.12.

For an ordinary annuity with semi-annual payments, if the payments began on April 1, 2012, when will the seventh payment be made?

Any help would be appreciated. thanks

Obviously from April 1, 2012 to April 1, 2016 is exactly 4 years. Since the payments are semi-annual, this, of course, means that there would be 4 X 2=8 payment, the last payment being on April 1, 2016. So, one semi-annual payment LESS, would be 6 months earlier, or Oct. 1, 2015, which is your answer.

i think it will be {12}~{cm}

~ it s need to mean aproximetly

semi annual mean 1/2 year-6 months