Question

Ok, last one for the night. I promise. I've been working on this darn problem for a few hours and I keep coming up with either 0, or -8.
The problem is: Iodine has a half life of 8 days. How long will it take for the iodine to be at 10%. The Initial amount is 100. Have to use th exponential decay model A=Ie^rt and use the half life to find the rate of decay. I have done this already, which is -0.0866434, but when I'm trying to find how long it'll take for the iodine to reach 10%, I keep coming up with 0. I'm attaching my work.

Answer 1

You have the correct value for r. Let's use that to find the value of t when A = 0.1I


A = Ie^(rt)


A = Ie^(-0.0866434t)


0.10I = Ie^(-0.0866434t)


0.10I/I = e^(-0.0866434t)


0.10 = e^(-0.0866434t)


ln(0.10) = ln(e^(-0.0866434t))


ln(0.10) = -0.0866434t*ln(e)


ln(0.10) = -0.0866434t*1


ln(0.10) = -0.0866434t


ln(0.10)/(-0.0866434) = t


t = ln(0.10)/(-0.0866434)


t = 26.575424


So it will take about 26.575424 days

Answer 2

Thank you, I acutally worked this problem out right before you posted this and got the same answer (26.575424 days) That just confirms it for me though. Thanks!

Answer 3

You're welcome. I'm glad you got the same answer and that you know what you're doing. Congrats.

Answer 4

yes, thank you!! I really appreciate you taking the time to help me though!

Answer 5

sure thing