ALGEBRA 2, 2012

 PAGE: 537 SET: Exercises PROBLEM: 1

The half-life of potassium- is billion years.

a.

Find the value of and the equation of decay.

Let is a intial amount of substance, then the amount that remains after billion years can be represents the .

(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 )

Thus, the equation for the decay of potassium- is .

b.

Find the how long will take the speciman to decay to only milligrams of potassium-.

Here and milligrams of potassium-.

(Substitute and )

(Divide each side by )

(Cancel common terms)

(Take ln on each side)

()

(Substitute: )

(Divide each side by )

(Cancel common terms)

It will take the specimen about years to decay to only milligrams of Potassium-.

c.

Find  how many milligrams of potassium- will be left after million years.

Here milligrams of potassium- and  years.

(Substitute and )

(Multiply exponents)

(Use caluculator: )

(Simplify)

About milligrams of Potassium- will be left after million years.

d.

Find how long will take Potassium- to decay to one eight of its original amount.

(Substitute )

(Divide each side by )

(Cancel common terms)

(Take ln on each side)

()

(Substitute: )

(Divide each side by )

(Cancel common terms)

It will take years to decay to one eighth of its original amount.

a. The equation for the decay of potassium- is .

b. It will take the specimen about years to decay to only milligrams of Potassium-.

c. milligrams of Potassium- will be left after million years.

d. It will take years to decay to one eighth of its original amount.

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