Question

A 41-gram sample of a substance that's used to detect explosives has a k-value of 0.139. Find the half-life in days.

Answer 1

same formula as before

N = N_0 ( e^(-kt))

N_0 = 41
N = 41/2 = 20.5
k = 0.139

Answer 2

N = N_0 ( e^(-kt))

20.5 = 41 * e^(-0.139)t

0.5 = e^(-0.139)t

ln(0.5) = -0.139t

Answer 3

so... 20.5=41^0.139t

Answer 4

yeah just don't forget the e

Answer 5

whats the e?

Answer 6

e is a constant that is (approximately) equal to 2.71828

Answer 7

oh ok

Answer 8

but you don't need to worry about it since it gets eliminated

Answer 9

taking the natural log will "undo" the e

Answer 10

cool

Answer 11

so if we have:

ln(0.5) = -0.139t

t = ln(0.5)/-0.139 = 5.0 days (depending on how they want you to round it)

Answer 12

my calc gives me 4.98667036374

Answer 13

days?

Answer 14

I think so

Answer 15

y does that look so easy... then u try it and its not

Answer 16

hm

Answer 17

no its just hard for me to learn something new with my ADD

Answer 18

ah, I see

Answer 19

wait im tryin to do one bms... after i divide both sides by N then what

Answer 20

you need to divide both sides by N_0 not N

Answer 21

you should get 0.5 on the left side and e(-something) on the right side

Answer 22

then you have:

0.5 = e(-kt)

take the natural log of both sides

Answer 23

ok
i got it

Answer 24

how do i get rid of the e?

Answer 25

when you take the natural log you can eliminate e since ln(e) = 1

Answer 26

so it would be N=-kt?

Answer 27

the ln(0.5) is still there

Answer 28

ln(0.5) = -kt

Answer 29

oh ok

Answer 30

then you just divide both sides by -k to get t

Answer 31

t = ln(0.5)/k, then just plug into your calculator

Answer 32

if the question asks for k instead it would be

k = -ln(0.5)/t

Answer 33

what about the negative before the k?

Answer 34

you can just divide both sides by -1, which will "move" the negative sign over

Answer 35

ln(0.5) = -kt

divide both sides by -1 gives

-ln(0.5) = kt

Answer 36

** I made a typo earlier

Answer 37

so u still divide by -k?

Answer 38

yeah

Answer 39

ln(0.5) = -kt

dividing by -k gives us

-ln(0.5)/k = t

Answer 40

how do i get rid of the negative sign bc i dont think it would be -...days

Answer 41

ln(0.5) is also negative, so -ln(0.5) is positive

Answer 42

-ln(0.5) = negative * negative = positive

Answer 43

oh duh lol

Answer 44

im gonna close this and do my other question can u just tell me if im doin it right?

Answer 45

sure

Answer 46

thx