SOLUTION: Please help with: Suppose you have 500 grams of a radioactive element whose half-life is 72 years. a. Find the function for the quantity, Q left in T years. b. FInd to the

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Please help with: Suppose you have 500 grams of a radioactive element whose half-life is 72 years. a. Find the function for the quantity, Q left in T years. b. FInd to the       Log On


   



Question 331673: Please help with:
Suppose you have 500 grams of a radioactive element whose half-life is 72 years.
a. Find the function for the quantity, Q left in T years.
b. FInd to the nearest thenth of a year when there will be 100 grams left.

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose you have 500 grams of a radioactive element whose half-life is 72 years.
:
a. Find the function for the quantity, Q left in T years.
Q = 500*2^(-t/72)
:
b. FInd to the nearest tenth of a year when there will be 100 grams left.
Q = 100
500*2^(-t/72) = 100
Divide both sides by 500
2^(-t/72) = 100%2F500
2^(-t/72) = .2
Find the log of both side:
log(2^(t/72)) = log(.2)
log equiv of exponents
-t%2F72log(2) = log(.2)
-t%2F72 = log%28.2%29%2Flog%282%29
using a calc:
-t%2F72 = -2.322
t = -2.322 * -72
t = 167.2 years