## x3_drummerchick one year ago 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.)

1. x3_drummerchick

@Nnesha

2. x3_drummerchick

@Jhannybean

3. x3_drummerchick

@dan815

4. dan815

okay so basically

5. dan815

we keep losing 1/2 ever 30 seconds

6. x3_drummerchick

i found the 'r' by doing ln2/30

7. dan815

wait i have to figure it out too

8. dan815

|dw:1443224796743:dw|

9. dan815

|dw:1443224894019:dw|

10. dan815

then we multiply 30*n to see how many seconds

11. x3_drummerchick

im confused

12. dan815

okay let me see how to explain this

13. x3_drummerchick

oohhh wait wait i think i know what you mean

14. x3_drummerchick

15. x3_drummerchick

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

16. dan815

yep

17. x3_drummerchick

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

18. 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

19. x3_drummerchick

Okay

20. dan815

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

21. x3_drummerchick

okay

22. dan815

|dw:1443225179484:dw|

23. x3_drummerchick

okay that makes sense

24. x3_drummerchick

so how would we incorporate that into the formula?

25. x3_drummerchick

|dw:1443225321392:dw|

26. dan815

okay

27. x3_drummerchick

|dw:1443225534573:dw|

28. dan815

every 30 secs u want a new half lige so

29. dan815

life

30. x3_drummerchick

okay

31. dan815

|dw:1443225561434:dw|

32. dan815

i believe this works

33. dan815

let me thing hmm

34. dan815

think

35. x3_drummerchick

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

36. x3_drummerchick

i dont know if that helps any

37. dan815

gimme a few mins, i am dealing with someone here

38. x3_drummerchick

okay

39. dan815

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

40. x3_drummerchick

okay thanks!

41. x3_drummerchick

actually i think i figured it out!

42. dan815

waiitt okay

43. dan815

i want to show u something important first

44. dan815

are you there

45. x3_drummerchick

crap, nvm i got it wrong

46. dan815

okay remember the (1/2)^n formula

47. x3_drummerchick

yeah

48. dan815

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

49. dan815

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

50. dan815

now u see every 30 secs we would exactly half it

51. dan815

the equation they give u is this just in disguise

52. x3_drummerchick

that makes sense

53. dan815

like for example

54. dan815

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

55. dan815

lets apply to that equation we know has to be right

56. x3_drummerchick

okay

57. dan815

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

58. dan815

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

59. x3_drummerchick

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

60. x3_drummerchick

front *

61. dan815

|dw:1443226339275:dw|

62. dan815

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

63. dan815

equivalent

64. dan815

there is only 1 rule im applying here over and over

65. dan815

|dw:1443226451939:dw|

66. x3_drummerchick

yes i do remember those

67. dan815

okay go ahead fill it all in now

68. x3_drummerchick

|dw:1443226609625:dw|

69. dan815

yes that is correct

70. dan815
71. x3_drummerchick

i got 79.33, is that right?

72. x3_drummerchick

seconds

73. dan815

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

74. x3_drummerchick

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

75. dan815

okay you're welcome :)