How much aspirin will remain from the 256 milligrams after 105 minutes?

Question

the half-life of asprin in a person's bloodstream is about 15 minutes. if a person's bloodstream contains 256 miligrams of asprin, how much of that asprin will remain after 105 minutes?

Answer 1

A(t) = B(1/2)^(kt)

 

A(0) = B(1/2)^(k*0) = B

 

A(t) = A(0)(1/2)^(kt)

 

1/2 = 1(1/2)^(15k)

 

15k = 1

 

k = 1/15

 

A(t) = A(0)(1/2)^(t/15)

 

A(105) = 256(1/2)^(105/15)

 

A(105) = (2^8)(1/2)^(7)

 

A(105) = (2^8)/(2^7) = 2 mg