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 P****otassium- 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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