I have determined a halflife function to be P(t) = 100((1/2)^(t/5730)), where P(t) is the percentage of C14 remaining, and "t" is the elapsed time.
Now, I am given the value P(t)=70, and am expected to solve for t.
Have I properly converted this?
70 = 100(1/2)^(t/5730))
(t/5730) = log(100(1/2))70
t = 5730(log(100(1/2))70)
Also, my calculator doesn't properly convert logarithms. My guess is it already has an assigned base value. How would I change this?
The value I got when doing this was:
~681456.9
It should be around 3000...
Homework Help
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Homework Help
I see.
What?
That you don't.
What?
That you don't.
Re: Homework Help
70 = 100(1/2)^(t/5730))
(t/5730) = log(100(1/2))70
The second line doesn't follow from the first.
Re: Homework Help
The problems are between these steps. I'm not sure how you got from one to the other. First of all, things are shuffling around between both sides of the equation like nobody's business. Second, it is not true that [imath]\log(ab^n) = n\log(ab)[/imath].70 = 100(1/2)^(t/5730))
(t/5730) = log(100(1/2))70
To convert from one base of logarithm to another, just use the change of base formula:
[math]\log_b a = {\log_c a \over \log_c b}[/math]
Use your calculator's log in place of [imath]\log_c[/imath].
EDIT: I should note that your answer is wrong for reasons unrelated to the base that your calculator uses. I just thought I'd explain anyway.

 Posts: 22
 Joined: Sun May 09, 2010 1:37 pm UTC
Re: Homework Help
It's not so much that I am have multiple bases, it's just that I don't know how to go from A to B in this case, isolating "t" in 70 = 100((1/2)^(t/5730))
Could someone show me how to isolate t?
Could someone show me how to isolate t?
I see.
What?
That you don't.
What?
That you don't.
Re: Homework Help
Assasinof6 wrote:Could someone show me how to isolate t?
Would you mind showing your work between the two steps people have commented on? If we see where exactly you're going wrong we can help you correct it.
double epsilon = .0000001;
 The Scyphozoa
 Posts: 2871
 Joined: Sun Jun 01, 2008 6:33 pm UTC
 Location: Sector 5
Re: Homework Help
70 = 100(1/2)^(t/5730))
(t/5730) = log(100(1/2))70
This is correct, it's just that it looks like multiplication when it's actually defining the base of the log.
(t/5730) = log{100*1/2}70
Imagine 100*1/2 to be a subscript. Or imagine
(t/5730) = (log 70)/(log 100*1/2)
And yes, to change the base of your logexample: you want to do log base b of ayou do log a / log b. If there is no log{b}a button, the base is probably 10.
I'm actually surprised how often I see people on these forums unable to sort through minor notation errors. Like one instance in the math jokes thread, where someone was trying to "prove" that studying is evil. It came to a part where the value (the word) "absolute" was being multiplied by two other "variables" on each side of the equation, and most people couldn't grasp that "absolute" was a variable and didn't mean word.
3rdtry wrote:If there ever is another World War, I hope they at least have the decency to call it "World War 2: Episode One"
doogly wrote:murder is a subset of being mean
Re: Homework Help
The Scyphozoa wrote:70 = 100(1/2)^(t/5730))
(t/5730) = log(100(1/2))70
This is correct, it's just that it looks like multiplication when it's actually defining the base of the log.
(t/5730) = log{100*1/2}70
Imagine 100*1/2 to be a subscript. Or imagine
(t/5730) = (log 70)/(log 100*1/2)
And yes, to change the base of your logexample: you want to do log base b of ayou do log a / log b. If there is no log{b}a button, the base is probably 10.
I'm actually surprised how often I see people on these forums unable to sort through minor notation errors. Like one instance in the math jokes thread, where someone was trying to "prove" that studying is evil. It came to a part where the value (the word) "absolute" was being multiplied by two other "variables" on each side of the equation, and most people couldn't grasp that "absolute" was a variable and didn't mean word.
Well, before you act all condescending  you're still wrong. It would still not work like that. There is a distinct difference between 100(1/2)^(t/5730) and (100(1/2))^(t/5730).
 The Scyphozoa
 Posts: 2871
 Joined: Sun Jun 01, 2008 6:33 pm UTC
 Location: Sector 5
Re: Homework Help
Syrin wrote:The Scyphozoa wrote:70 = 100(1/2)^(t/5730))
(t/5730) = log(100(1/2))70
This is correct, it's just that it looks like multiplication when it's actually defining the base of the log.
(t/5730) = log{100*1/2}70
Imagine 100*1/2 to be a subscript. Or imagine
(t/5730) = (log 70)/(log 100*1/2)
And yes, to change the base of your logexample: you want to do log base b of ayou do log a / log b. If there is no log{b}a button, the base is probably 10.
I'm actually surprised how often I see people on these forums unable to sort through minor notation errors. Like one instance in the math jokes thread, where someone was trying to "prove" that studying is evil. It came to a part where the value (the word) "absolute" was being multiplied by two other "variables" on each side of the equation, and most people couldn't grasp that "absolute" was a variable and didn't mean word.
Well, before you act all condescending  you're still wrong. It would still not work like that. There is a distinct difference between 100(1/2)^(t/5730) and (100(1/2))^(t/5730).
Oooh... you're right, I didn't catch that. Thanks.
So in that case it would be
7/10=(1/2)^(t/5730)
log{1/2}(7/10)=(t/5730)
3rdtry wrote:If there ever is another World War, I hope they at least have the decency to call it "World War 2: Episode One"
doogly wrote:murder is a subset of being mean
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