Math help [Click Melody]

Vraces:

A radioactive kalashnikov gets less radioactive every year. After 60 years only 25% of the radio-activeness remains.
What is the yearly reducing of radio-activeness in percent?

Hi Vraces,
You have to let r be a decimal . That is, if it was 2% then r=0.02 (that's just an example)

S is future value, P is present(or original) value, r is yearly rate reduction and n is the number of years.

S=P(1-r) ⁿ

Now, when n=60, S=P/4, find r

You see if you can finish it.

I don't understand what you mean by P and S.

Vraces:

I don't understand what you mean by P and S.

P is the original value. it is how much radioactivity was there to start with.
S is how much radioactivity is there after n years have passed.

In your question, you don't know how much radiactivity was there at the beginning but you know that after 60years only 0ne quarter of it will be left.

I suggested that you leave P as the original value and then S is one quarter of P that is P/4. (The Ps cancel out almost straight away anyhow)

You could just as well say that the original amount P is 4, in which case the end amount S would be 1
you could use any of these
P=8, S=2
P=20 S=5
P=300, S=75
So long as the future value S is one quarter the value of the original value P you can use whatever numbers you like.

Does that help?
I'm off to bed soon so you better be quick but I'll give you a few minutes to think about it.

PS I don't mind you using my name in the title, I'm surprised that no one else has ever done it, but a please would be nice

you have to turn this into an equation. when x is 60, y is 25,so divide both sides by 60 to find how much radiation is lost each year. 60/25=2.4. so 2.4% of radiation is lost each year.

CrustySandwich:

you have to turn this into an equation. when x is 60, y is 25,so divide both sides by 60 to find how much radiation is lost each year. 60/25=2.4. so 2.4% of radiation is lost each year.

Hi Crusty,
what makes you think that y is 25 when x is 60?

Right I get it now.

And sorry about that "[Click Melody]". It sounded much nicer in my head at the time. I'm going to solve it a little later I'm currently busy. Thanks for the help Melody and you other one that just commented.

0.25 = 1(1-r)^n
0.25 = 1+r^60
-0.75 = r^60
r = - 0.75^(1/60) = 0.016666...7
r = [ Incorrect]
My calculation and understanding is completely off. If you spoke to me in math maybe I could understand better.

And sandwich man, your answer is incorrect, I thought that too at first. That is almost the answer, but almost doesn't cut it if we're talking math. Thanks for trying though.

Vraces:

0.25 = 1(1-r)^n
0.25 = (1-r)^60
-0.75 = r^60
r = - 0.75^(1/60) = 0.016666...7
r = [Incorrect]
My calculation and understanding is completely off. If you spoke to me in math maybe I could understand better.

And sandwich man, your answer is incorrect, I thought that too at first. That is almost the answer, but almost doesn't cut it if we're talking math. Thanks for trying though.

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Your calculation and understanding are not completely off! You just took away the bracket too soon. I don't know why you did that
If I spoke to you in person you could understand much more easily. I am an excellent teacher. (That's what I think anyway)
But there is always a time delay on the web that slows everything down and makes learning (and teaching) harder.
However;
Sometimes I think that things are remembered better if the learning part is more of a trial.

0.25 = (1-r )^60
0.25^(1/60) = 1-r
r = 1 - (0.25)^(1/60)
r = 0.022840031
r = 2.28% (3 significant figures)

Right! I was taking 0.75^(1/60) for some reason. Anyways thanks for helping me out, I get it now.