Question

can someone help me with my problem?

Answer 1

and what is your problem jmfranco?

Answer 2

2) We often use radio-isotopes to estimate the age of things (such as the
Earth). Assuming the half-life of some isotope is 1000 years, and you
found a rock of unknown age near the Mid Atlantic Ridge. You measured
the amount of isotope in the rock and determined that 12.5% of the
original amount when the rock formed was still present. How old is the
rock

Answer 3

Let's have a chat here franco. This is a growth and decay problem. Is that the topic you're studying?

Answer 4

ok..yes it is

Answer 5

great. now, sometimes growth and decay have been modeled by exponential functions. This is the model common model and the one you'll be using here.
Do you know the form of the exponential function that is used to model growth and decay? is so, type it in here...

Answer 6

I hope you don't mind that I'm not just giving you the answer, but you'll be better able to solve all the other problems you'll have this way. it will only take a few minutes.

Answer 7

okay i don't really know exponential. i understand

Answer 8

r us still there?

Answer 9

yes, i'm here

Answer 10

my connection just failed me for a bit, but i'm back

Answer 11

this website is having a lot of traffic and seems slow, check out this site has a good explanation: http://serc.carleton.edu/quantskills/methods/quantlit/expGandD.html

Answer 12

take a look and let me know if you have any questions

Answer 13

please let me know once you have briefly looked at the page...

Answer 14

then we can choose between those two equations and use the information you were given to solve the problem. it's not hard at all and you'll see.

Answer 15

ok looked at it its sort of complicated can u go step by step

Answer 16

sure

Answer 17

so the two functions are n(t) = n0*e^(kt)

Answer 18

now, the exponent of e is that decides whether we have a growth or decay. If it is negative, then the graph starts high and comes down (decay) and the opposite is true if the exponent is positive.

Answer 19

with me so far?

Answer 20

yes

Answer 21

by the way, what grade you in? so I know what you sort of should know...

Answer 22

college lol

Answer 23

hehe, no worries. I just graduated a year ago myself. any how...i hope you're not rushed cuz I'm definitely not moving very quickly...let me know if you're rushed.

Answer 24

so let's go over the equation in more detail...

Answer 25

the site gives good description for each variable involved.

Answer 26

lol cool. well i got this question and another, these questions r complicated and due at 4

Answer 27

today sorry don't rush its okay.

Answer 28

I'm gonna ask you to rephrase them for me here: what does N(t) mean? and the N_0(t) (that is the subscript zero), the k? the t?

Answer 29

once you have those, we can replace the variables with the information in your problem. I just wanna make sure you're with me...

Answer 30

Nt is quatity in time, t is time,n0 is initial quantity, k is a constant and eX is exponential function

Answer 31

good

Answer 32

so, it's N(t) and it is a function of time. It's very important that you understand that. and eX is e^(x) which is the mathematically constant e (approx 2.71..) to power x.

Answer 33

okay

Answer 34

so what the formulate says is N(t) [the amount as a function of time] = n0*e^(k*t) [the original amount times the exponential function to power k times t]

Answer 35

k here is the rate of change. the larger is it, the faster the amount grows or, in this case, decays.

Answer 36

What is the question asking of us? what do you think will be the variable that will be the final answer?

Answer 37

stay with me franco, we're almost there

Answer 38

not sure ive never done a prblem like this one

Answer 39

the question asks you how old is the rock when only 12.5% of it is left..

Answer 40

so we're looking for time, which will be contained in our variable t.

Answer 41

a clue that is give to you without knowing it is the term "half-life"

Answer 42

how long is the half-life of this rock?

Answer 43

Franco?

Answer 44

1000

Answer 45

thank you.

Answer 46

so that means that in a 1000 years, we'll only have 50% of the original material left. that IS what half life means.

Answer 47

okay so what do i do??

Answer 48

so let's set up the equation

Answer 49

actually, I'll let you do it: in 1000 years, we will only have 50% of the original material. can you set that up?

Answer 50

i'll prompt with good questions:
first: what is t?

Answer 51

nooo :( i don't kno how this is complicateddd!

Answer 52

okay: time in this case is 1000 years.
second: notice how you can divide both sides by n0 (the original material) - once we do this, what do we have on the left side of the equation?

Answer 53

this is only solving the first component of the problem.any way, when we divide both sides by n0, we get the equation: N(t)/n0 = e^(kt)

Answer 54

are you with me?

Answer 55

in a thousand years, we know we will only have half left, so what will N(t)/n0 equal? think about this one cause it solves 50% of the problem!

Answer 56

Franco? are you still with me?

Answer 57

is n0 1000

Answer 58

i didvide both sides by that?

Answer 59

n0 is the original amount. was that given in the probem? 1000 is the number of years...

Answer 60

before i loose you here, we divide the variable n0 by both sides so that we can remove it from the right side and put it on the left. you understand what this results in?

Answer 61

I miss half life problems, what is that calculus 1

Answer 62

no what is the asnwer/

Answer 63

now the equation looks like this: \[n(t) \div n _{0} = e ^{k*t}\]

Answer 64

no, there is no calculus involved. this is still pre-calc

Answer 65

do you understand how we get that equation?

Answer 66

how do you know so much about math thierryu

Answer 67

I studied engineering in college, i just graduated last year

Answer 68

are you here to help us Amanda?

Answer 69

Franco, do you see how we got that last equation I put in?

Answer 70

yes

Answer 71

good

Answer 72

Now, if it has been a 1000 years and we only have 50% of the original materia.

Answer 73

so now if t=1000, we're gonna look at n0/N(1000). All we know about this fraction is that N(t) at t=1000 is 50% of n0, the original amount.

Answer 74

digest that.

Answer 75

therefore, N(t)/n0 when t=1000 years should give us 1/2. do you agree?

Answer 76

I meant to say N(t)/n0 all along. sorry for the confusion.

Answer 77

bradley, you found me here!

Answer 78

should just got to wolfram mathmatica, and type in halflife

Answer 79

Franco, are you with me? do you see why N(t)/n0 at the half-time (t=1000) will give us 1/2 ?

Answer 80

so wats the answer??? yea i see

Answer 81

i did but i will let you help him first

Answer 82

alright. so now we have 1/2 = e^(k*t)

Answer 83

im a girl

Answer 84

and t= 1000 so we really have .5=e^(1000k)

Answer 85

franco plug in your time and your values for n and No

Answer 86

ok

Answer 87

now we solve for k by first takiing the natural log of both sides:
ln(.5) = ln(e^(1000k))

Answer 88

we do this because we know that the ln(e^(x)) equals x.

Answer 89

so ln(e^(1000k)) reduces to simply 1000k!

Answer 90

now you can use your calculator to solve for k from teh equation: \[\ln(.5) = 1000*k\]

Answer 91

what is k?

Answer 92

once you find k, we go back to the board, but now we have everything we need expect time which is exactly what we're looking for!

Answer 93

umm not sure..

Answer 94

why? because we only have 12.5% left. so the ratio of N(t)/n0 = .125

Answer 95

you're not sure about k?

Answer 96

there you'd just use a calculator; get the natural log of .5 and then divide it by 1000

Answer 97

are you with me now?

Answer 98

i know this was elongated by if you go over this chat and solve the same or a similar problem, you'll get a hang of it. don't be discouraged.