SOLUTION: Sodium-24 is a radioactive isotope of sodium that is used to study circulatory dysfunction. Assuming that 4 micrograms of sodium-24 are injected into a person, the amount A in micr

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Sodium-24 is a radioactive isotope of sodium that is used to study circulatory dysfunction. Assuming that 4 micrograms of sodium-24 are injected into a person, the amount A in micr      Log On


   

Question 1006212: Sodium-24 is a radioactive isotope of sodium that is used to study circulatory dysfunction. Assuming that 4 micrograms of sodium-24 are injected into a person, the amount A in micrograms remaining in that person after t hours is given by the equation A = 4e^−0.046t.
(b) What amount of sodium-24 remains after 8 hours? (Round your answer to two decimal places.)

=µg
(c) What is the half-life of sodium-24? (Round your answer to two decimal places.)

=h
(d) In how many hours will the amount of sodium-24 be 1 microgram? (Round your answer to two decimal places.)

=h
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
The decay model written better, highlight_green%28A=4e%5E%28-0.046t%29%29.

(b)
After 8 hours, just plug-in t=8 and compute A.

(c)
Very simply choose 1%2F2=1%2Ae%5E%28-0.046%2At%29 to find half-life.
ln%281%2F2%29=ln%281%29%2B%28-0.046t%29ln%28e%29
-ln%282%29=0-0.046t%2A1
ln%282%29=0.046t
highlight%28t=ln%282%29%2F0.046%29
Compute to
highlight%28t=15%29, in HOURS

(d)
This is similar to finding half-life.
You want A=1, and again find logarithms of both sides of the decay equation, to
solve for t.
ln%281%29=ln%284%29%2B%28-0.046t%29ln%28e%29
0=ln%284%29-0.046t
0.046t=ln%284%29
highlight_green%28t=ln%284%29%2F0.046%29
and you can finish the computing.