SOLUTION: Hello dear tutor, I need help with a certain math problem today that we just learned in class, but I can only get how to do really with like an actual example from my homework, w

Question 179440: Hello dear tutor,
I need help with a certain math problem today that we just learned in class, but I can only get how to do really with like an actual example from my homework, which is why I am here, trying to learn! So here is the question! Thanks so much for helping out! it means ALOT!

Radon-222 is a gas that escapes from rocks and soil. It can accumulate in buildings and can be dangerous for people who breathe it. Radon-222 decays to polonium and eventually to lead.

a. Find the percent decrease in the amount of radon-222 each day.
b. Write an exponential decay function for th amount of a 500 mg sample of radon-222 remaining after t days.

c. How much of the radon-222 sample would remain after 14 days?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
You left this out of your post but it is essential information for your problem: "The most stable isotope, 222Rn, has a half-life of 3.8 days"
-------------
Radon-222 is a gas that escapes from rocks and soil. It can accumulate in buildings and can be dangerous for people who breathe it. Radon-222 decays to polonium and eventually to lead.
a. Find the percent decrease in the amount of radon-222 each day.
---
Percent means per hundred
So set up a proportion and solve for "x":
x/100 = (1/2)/3.8
Cross-multiply to get:
3.8x = 50
x = 12.88
Ans: 12.88%
---------------------------
b. Write an exponential decay function for the amount of a 500 mg sample of radon-222 remaining after t days.
General Formula: A(t) = A(0)*(1/2)^(t/3.8)
Your problem:
A(t) = 500(1/2)^(t/3.8)
----------------------------
c. How much of the radon-222 sample would remain after 14 days?
A(14) = 500(1/2)^(14/3.8)
A(14) = 500(1/2)^3.6842..
A(14) = 500*0.0777933...
A(14) = 38.8967.. mg
===============================================
Cheers,
Stan H.

RELATED QUESTIONS
Hello dear tutor, I need help with a certain math problem today that we just learned in (answered by josmiceli)

Hello dear tutor, I need help with a certain math problem today that we just learned... (answered by stanbon)

Dear tutor, Im in the ninth grade.In my math class today we learned how to slove compound (answered by tutorcecilia)

Hello I have a lot of math to do for homework and I forgot how to do it since we just... (answered by josgarithmetic)

My daughter needs help with math she starts 6th in 5 days and wants to understand math to (answered by oscargut)

Hello my name is Aaliyah and I really need help on this problem. 2x-5y=-158 x-y=-40... (answered by nerdybill,feliz1965,stanbon)

Ok so today i have just started high school, my 3rd high school, and in class today my... (answered by stanbon)

Dear Tutor, So, I am in Geometry, and we are starting trig. The question is "Points... (answered by Alan3354,josgarithmetic,macston)

Please help me with this. The directions say to Find is foci. Today in class we... (answered by Mathtut)