ALGEBRA 2, 2012
11

 PAGE: 538 SET: Exercises PROBLEM: 11

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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