I'm this ___ far away from just not doing this homework all together because you people make things too complicated. The way we're supposed to solve the question is with the formula A(.5)^T The QUESTION is If a substance has a half life of 72 hours how many days will it take to reach 10% of its original amount? Q #2: How many days until 70% is left?
I really want to understand this.
2006-09-18 13:22:56 · 6 answers · asked by guardian_erin 2 in Science & Mathematics ➔ Mathematics
This problem is just straight exponentiation and logarithms. Do you know your logarithm rules?
If the halflife is 72 hours (3 days) then that means that:
0.5 = A * (0.5)^(3)
Solve for A. Got it? Good! Now you have your formula.
Time to reach 10%? 10% is 0.1, so
0.1 = A * (0.5)^T
You know A, solve for T. Got it? Good. That is answer 1.
Time to reach 70%?
0.7 = A * (0.5)^T
Again, solve for T. Got it? Good. That is answer 2.
2006-09-18 13:35:43 · answer #1 · answered by BalRog 5 · 1⤊ 3⤋
Ok, just set up your equation like this.
A = Ao*(1/2)^(T)
where:
A = amount of stuff remaining
Ao = original amount of stuff before decaying started
T = number of half-lives that have passed (3-day periods)
#1
When 10% of the original amount is remaining A = 0.1*Ao.
So:
0.1*Ao = Ao*(1/2)^(T)
0.1 = (1/2)^T
#2
When 70% of the original amount is remaining A = 0.7*Ao.
So:
0.7*Ao = Ao*(1/2)^(T)
0.7 = (1/2)^(T)
For both problems, just take the log base (1/2) of each side. This makes the (1/2)^(T) on the right side turn into T (think about the definition of a logarithm a while and you will understand why). Then use the change of base formula to find the logs with base (1/2) using your calculator on the left side. eg: ln(.1)/ln(1/2)
Now you have solved for T (number of half-lives). To find the number of days, just remember that there are 3 days per half life.
2006-09-18 13:40:41 · answer #2 · answered by Ubi 5 · 1⤊ 1⤋
May be you can get somebody in your class that understands it better to explain it to you if you're not satisfied here.Remember not everyone on here knows how to do your homework exactly the way you want it we're just trying our best to help!!!!!!!!
2006-09-18 13:27:27 · answer #3 · answered by Ali.D 4 · 0⤊ 0⤋
You'll always miss 100% of the shots you don't take, and, statistically speaking, 99% of the shots you do.
2006-09-18 13:47:37 · answer #4 · answered by Sam 7 · 0⤊ 1⤋
Sorry i can't help on your hemework but if you don't at least give it a try then you will quite probably fail the class.
2006-09-18 13:25:47 · answer #5 · answered by Sniper 4 · 1⤊ 1⤋
1. 129.6 hours
2. 100.8 hours
hope this helps :-)
.
2006-09-18 13:27:12 · answer #6 · answered by sisbromomdad 2 · 0⤊ 3⤋