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The substance decay is of its total mass after years.
a.
Find the half-life of substance.
The substance decay is then .
(Exponential decay formula)
(Substitute and )
(Divide each side by )
(Cancel common terms)
(Take ln on each side)
()
(Divide each side by )
(Cancel common terms)
(Substitute: )
(Simplify)
(Substitute )
Let is a intial amount of substance, then the amount can be represents the .
(Exponential decay at )
(Substitute )
(Divide each side by )
(Cancel common terms)
(Take ln on each side)
()
(Substitute: )
(Divide each side by )
(Cancel common terms)
The half–life of the substance is about years.
The half–life of the substance is about years.
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