Raymond B. answered • 11/13/22
Math, microeconomics or criminal justice
half life is 4 days
after 20 days just 2 mg left
how much was there originally? the Big Question.
God (Allah, your deity choice of the day, or the secular Force. see that GI movie starring the Rock) only knows. OMG or maybe a few obtuse pathetic mathematicians know too. never know. so far no one's even figured out the problem much less the answer. the problem is often figuring out what the problem is. call it compounding. pound sand.
A =Pe^rt is the basic formula. decay rates are continuously compounded. It's nature's way. God knows why. Maybe Nature knows. r=decay rate, t=time, A =ending amount, P = starting amount. ending amount=half starting amount for half life time (not the half time superbowl festivities & commercial breaks, much more entertaining though)
1/2 = e^4r for half life with 4 days, r= decay rate
take natural logs of both sides
ln.5 = 4r
r= ln.5/4 = about -.7/4 = about -.1733
=about =-.1733x24 = about -4.16 hours approximately = the decay rate, every 4 days half left, not every 4 hours half left
A= Pe^-.1733t
2 =Pe^-.1733(20)
P = ln2/e^-.1733(20)
= about .7/-3.5 = -1/.5= -.2 = less than it decayed to? super major mistake somewhere. You start with the bigger amount then it decays leaving a smaller amount, Not the reverse
general method is right. calculations went south to Antarctica. Not even climate change helped. Save the penguins who may know far more math counting fish. Animals can count. Proven. beyond all doubt. Certain. Your dog knows more math than most people and whoever did the above numbers.
(sorry, I'm too obsessed with an impossible chemistry problem someone posted-- far worse. Avoid chemistry if the lab fumes are too much, as with lung problems, not to be mistaken for covid19 infections)
half life is 4 days
after 20 days it's down to 2 mg
that means in 16 days there was 4 mg. those last 4 days cut it in half
in 12 days 8 mg
in 8 days 16 mg
in 4 days 32 mg
at time zero, starting time, there were 64 mgs
each 4 days it decayed to half its amount
day zero 64 mgs
day 4, 32
day 8 16
day 12 8
day 16 4
day 20, 2 mg
it started with 64 mgs
find the mistake in the first calculations and you get 2 points extra credit plus a pat on the head and a dog treat for your dog who helped you find the error(s)
It's late on a Saturday night. Why aren't you in bed? Do your parents know where you are? What are you up to? Hard to believe you're doing math problems. Have a good explanation when you come home. Don't try to sneak in the window. You could get shot these days, by residents thinking you're a burglar. especially in big cities like NYC
