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| 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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