Question

Half - life

Stronium - 90 has a half - life of 28 days.

Answer 1

do you have an equation that models the decay...?

Answer 2

(a) A sample has a mass of 50 mg initially. Find a formula for the mass remaining after t days.
(b) Find the mass remaining after 40 days.
(c) How long does it take the sample to decay to a mass of 2mg?
(d) Sketch the graph of the mass function.

Answer 3

I'll find an equation - gee what a clever message board this is :-)

Answer 4

I just started this, so I'm kind of confused how to do it.

Answer 5

ok... so the model will be something like

\[A = P \times e^{-kt}\]

Answer 6

so you know the A =0.5 when t = 28 and P = 1

P is the intial quantity.... A is the quantity after t time periods and k is the growth constant

Answer 7

Here's a good page (and calculator) concerning half-lives
http://1728.org/halflife.htm
has formulas too

Answer 8

so

\[0.5 = 1 \times e^{-k \times 28}\]

you'll need to find k, using logs

Answer 9

hope it makes sense

Answer 10

Got ya

Answer 11

then when you know the value of k, you can then undertake the other parts of the question.

But thats on the proviso that the decay is exponential... and uses the model above

Answer 12

for part b)
Ending amount = beginning amount / 2^n
where n = time / half-life
Ending amount = 50mg / 2^(40/28)
Ending amount = 50 mg / 2^1.4285714286
Ending amount = 50 mg / 2.6918003853
18.5749286142 mg

Answer 13

Thanks wolf ^.^

Answer 14

well there you go, its a base 2 exponential equation rather than a base e equation...

Answer 15

k = ln2/28

Answer 16

u r welcome iambatman

Answer 17

-ln*

Answer 18

c) time to decay to 2 mg

time = (half-life) * log(begng amt / ending amt) / log (2)
time = 28 days * log(50/2) / log (2)
time = 28 days * log (25) / log(2)
time = 28 days * 4.6438561898
time = 130.0279733137 days or
about 130 days

Answer 19

Ah, thanks a lot!!

Answer 20

Wolf for part b I don't understand why you're dividing by 2^...

Answer 21

Thought it was just 50e^-0.025*40

Answer 22

Sorry for being away for a while.
Does someone need a graph?
(Okay now I'll work on your question).

Answer 23

Lol awesome

Answer 24

I get 18.394..

Answer 25

A little different from yours haha

Answer 26

That's okay :-)
As for the dividing by the two, basically when I wrote that calculator and those equations, I wanted something that could be stated in plain English and NOT
⌠ 0 --> ∞ as f(x) , etc (or whatever strange calculus symbols they use).

Answer 27

Is that for part b you are referring?

Answer 28

Yup

Answer 29

I used the formula y = 50e^-0.025t

Answer 30

Where does that .025 come from?

Answer 31

k = -ln2/28

Answer 32

Got 130 days as well woo, nice one wolf!

Answer 33

Thank you so much, especially for the graph!

Answer 34

okay I'm trying to redo part b) using your formula
So that should be
50 * e ^ -(ln(2)/28) ?

with ln(2) = 0.6931471806
and ln(2)/28 = 0.0247552564
so it would be e ^ -.0247552564

I get 0.9755486421 for that part

Answer 35

It's okay iambatman
I'm still trying to see what the difference is between your answer and mine for part b)

Answer 36

Oh I see it should be 50e^-0.025*40
e^-0.9902102579 = 0.3714985723
times 50 equals
18.5749286142

Answer 37

:p

Answer 38

So, I guess I was right?

Answer 39

Oh no your number is still the same lol

Answer 40

But I calculated the number the second time using your formula (check my math),

Answer 41

0.367879441

Answer 42

You're using exactly 0.025 right?

Answer 43

Heck no - (I wanted to see how we got different numbers).
So you said 0.367879441
whereas I calculated 0.3714985723

Answer 44

hahaha maybe that's why

Answer 45

I've been using exactly 0.025 XD

Answer 46

getting -1

Answer 47

Heck I had a feeling I was correct because I rechecked my calculations with the web page calculator.

Answer 48

I get -0.9902102579

Answer 49

Lol sorry about that, and did you use 0.025 and got that now?

Answer 50

No I used e^-0.9902102579
which equals 0.3714985723
then multiplying by 50 I got 18.5749286142

Answer 51

I have to get going be back in 15 minutes.
By the way, please check out my web site www.1728.org
it has some rather nice calculators

Answer 52

Alright later wolf, and awesome, I will definitely check it out.

Answer 53

Thanks again!