Question 331673
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) = {{{100/500}}}
2^(-t/72) = .2
Find the log of both side:
log(2^(t/72)) = log(.2)
log equiv of exponents
{{{-t/72}}}log(2) = log(.2)
{{{-t/72}}} = {{{log(.2)/log(2)}}}
using a calc:
{{{-t/72}}} = -2.322
t = -2.322 * -72
t = 167.2 years