Question

Find the half life of the following quantity;
x(t)=90+10^(-4t)

Answer 1

what does half life mean?

Answer 2

The time it takes for half of the substance to deteriorate.

Answer 3

Would I set x(t)=180, then take log base 10 of each side?

Answer 4

I'm used to half life problems that are stated in English : 50 gms decays to 43 grams in 6.2 years - that sort of thing.

Answer 5

They are usually stated in terms of exponential decay. To find the half life of y(t)=80*e^(-3t), for example, you would set y(t)=40. Then divide to get 1/2=e^(-3t). Then take the natural log of both sides to get -ln(2)=-3t, or t=ln(2)/3. I'm just not sure what to do when the equation is changed.

Answer 6

As stated, the problem makes no sense. 90 is constant. "half-life" is not a meaningful concept.

Answer 7

I'm usually very good at half life problems but I need to do some research on this.
First of all in the equation x(t)=90+10^(-4t) what is the '90' and what does the '4' represent? I'm guessing the x(t) is the half life.

Answer 8

That is all the information we are given. I'm assuming the -4 is the k, and 90 must be some sort of initial condition? I think x(t) is the half life as well.

Answer 9

It doesn't seem to make too much sense as it is written.

Answer 10

I'll do some research. As I said I'm pretty good at half life problems.
As a matter of fact, here is a page from my website:
www.1728.org/halflife.htm

Answer 11

Hmmm you can't post a link in here?

Answer 12

I just copied and pasted it into my browser, it worked.

Answer 13

Okay Melody :-)
Time for me to do some research.

Answer 14

Thank you! :)

Answer 15

Well I searched all over the internet and could not find any half life information that has a formula like this
x(t)=90+10^(-4t)
What a lousy way to phrase a question.
I suppose you could tell this to your instructor.


Well I tried. :-)

Answer 16

Thank you for trying! I just e mailed them and asked if it was perhaps a mistake, or to see if they could offer any tips.

Answer 17

I think it must have been a typo in the question.

Answer 18

Well you can always E-Mail them a question like " Since 60 miles per hour = 88 feet per second - when will the bus get to Philadelphia?"

Answer 19

hahahaha

Answer 20

I bet they would love that. Hopefully questions will be more clear in the future.

Answer 21

Yes, that might show them it is worth the time to state things as clearly as possible.

Well if you do get an e-mail please let me know.

see you Melody.

Answer 22

I'll let you know their response!

Answer 23

thanks :-)

Answer 24

The teacher just emailed me back, they changed the question to find the half life of 90*e^(-4*t). Much easier now!

Answer 25

I'm really interested in this now.
I found a formula:
P = A * e^(-time * ln(2)/half-life )
where p = present amount A = beginning amount and (ln(2)/half-life) is usually represented by 'k'.
So I'm guessing that in the formula
90*e^(-4*t)
'90' is the beginning amount
't' is the elapsed time and
-4 is k (ln(2)/half-life)

So, it seems to me that the question gives you the beginning amount and 'k' but to me wouldn't you also need the present amount to determine half-life ?