precal
posted by james on .
If the halflife of a certain radioactive substance is 2000 years, estimate how many years must elapse before only 35% of the radioactive substance remains?

For halflife question, a good equation to use is
amount = starting value (1/2)^(t/k) where k is the halflife
so :
.35 = 1(1/2)^(t/2000) , t in years
.35 = (.5)^(t/2000
log .35 = log ( (.5)^(t/2000)
log .35 = (t/2000) log .5
t/2000 = log .35/log .5
t = 2000( log .35/log .5) = 3029.14
it would take appr 3029 years