# Calculus

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Radius decays at a rate of that is proportional to its mass, and has a half-life of 1590 years. If 20 g of radium is present initially, how long will it take for 90% of this mass to decay?

• Calculus -

so you want 10% to remain (the 20g is actually not relevant)

solve
.1 = (1/2)^(t/1590)
log .1 = log (.5^(t/1590))
t/1590(log .5) = log .1
t/1590 = log .1/log .5
etc.

let me know if didn't get t = 5282

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