# precal

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If the half-life of a certain radioactive substance is 2000 years, estimate how many years must elapse before only 35% of the radioactive substance remains?

• precal -

For half-life question, a good equation to use is

amount = starting value (1/2)^(t/k) where k is the half-life

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

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