How do i solve this!? Will give medals!
Radium-221 has a half-life of 30 sec. How long will it take for 84% of a sample to decay? (Round your answer to the nearest whole number.)

- x3_drummerchick

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- x3_drummerchick

@Nnesha

- x3_drummerchick

@Jhannybean

- x3_drummerchick

@dan815

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## More answers

- dan815

okay so basically

- dan815

we keep losing 1/2 ever 30 seconds

- x3_drummerchick

i found the 'r' by doing ln2/30

- dan815

wait i have to figure it out too

- dan815

|dw:1443224796743:dw|

- dan815

|dw:1443224894019:dw|

- dan815

then we multiply 30*n to see how many seconds

- x3_drummerchick

im confused

- dan815

okay let me see how to explain this

- x3_drummerchick

oohhh wait wait i think i know what you mean

- x3_drummerchick

you start with 1 mg

- x3_drummerchick

i mean, 1 "sample" of it, right?

- dan815

yep

- x3_drummerchick

okay, and howd you get the (1/2)?

- dan815

okay so forget like the 30 secs to begin with i mean remember it but we really wanna see how many half lives have passed we just know 1 half live is 30 seconds keep that in mind

- x3_drummerchick

Okay

- dan815

basically like this, now you know that for every half life we multiply by a 1/2

- x3_drummerchick

okay

- dan815

|dw:1443225179484:dw|

- x3_drummerchick

okay that makes sense

- x3_drummerchick

so how would we incorporate that into the formula?

- x3_drummerchick

|dw:1443225321392:dw|

- dan815

okay

- x3_drummerchick

|dw:1443225534573:dw|

- dan815

every 30 secs u want a new half lige so

- dan815

life

- x3_drummerchick

okay

- dan815

|dw:1443225561434:dw|

- dan815

i believe this works

- dan815

let me thing hmm

- dan815

think

- x3_drummerchick

here is an example layout, but doesnr have answers, it confused me

##### 1 Attachment

- x3_drummerchick

i dont know if that helps any

- dan815

gimme a few mins, i am dealing with someone here

- x3_drummerchick

okay

- dan815

yeah dont worry ill help u understand this stuff its pretty simple

- x3_drummerchick

okay thanks!

- x3_drummerchick

actually i think i figured it out!

- dan815

waiitt okay

- dan815

i want to show u something important first

- dan815

are you there

- x3_drummerchick

crap, nvm i got it wrong

- dan815

okay remember the (1/2)^n formula

- x3_drummerchick

yeah

- dan815

now lets tweak that a little bit okay we know that for evert 30 secs we want it to be halved so

- dan815

1*(1/2)^(t/30)

- dan815

now u see every 30 secs we would exactly half it

- dan815

the equation they give u is this just in disguise

- x3_drummerchick

that makes sense

- dan815

like for example

- dan815

if we apply e^ln(x) = x
e and ln cancel out right

- dan815

lets apply to that equation we know has to be right

- x3_drummerchick

okay

- dan815

e^ln((1/2)^(t/30))

- dan815

do you know your ln rules like
ln(x^3)= 3 ln x the power multiples

- x3_drummerchick

oh wait, dont you bring it to the rfont of the ln?

- x3_drummerchick

front *

- dan815

|dw:1443226339275:dw|

- dan815

with a little bit of manipulation we see that the equation is exactly reuivalent

- dan815

equivalent

- dan815

there is only 1 rule im applying here over and over

- dan815

|dw:1443226451939:dw|

- x3_drummerchick

yes i do remember those

- dan815

okay go ahead fill it all in now

- x3_drummerchick

|dw:1443226609625:dw|

- dan815

yes that is correct

- dan815

http://prntscr.com/8kirao

- x3_drummerchick

i got 79.33, is that right?

- x3_drummerchick

seconds

- dan815

i am not using a calculator make sure u round it to the 10th

- x3_drummerchick

its correct :) thank you again so much, youre awesome!

- dan815

okay you're welcome :)

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