SOLUTION: The function C(t) = K(e^(-at) - e^(-bt)), where a,b,K are positive constants and b>a, is used to model the concentration at time t of a drug injected into the bloodstream. a.Find

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: The function C(t) = K(e^(-at) - e^(-bt)), where a,b,K are positive constants and b>a, is used to model the concentration at time t of a drug injected into the bloodstream. a.Find       Log On


   

Question 1026908: The function C(t) = K(e^(-at) - e^(-bt)), where a,b,K are positive constants and b>a, is used to model the concentration at time t of a drug injected into the bloodstream.
a.Find the limit of C(t) as t approaches infinity.
b.Find dC/dt, the rate of change of drug concentration in the blood.
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
a. Since b > a > 0, lim%28t-%3Einfinity%2C+e%5E%28-at%29%29+=+0 and lim%28t-%3Einfinity%2C+e%5E%28-bt%29%29+=+0, and solim%28t-%3Einfinity%2C+C%28t%29%29+=+0.
b. dC%28t%29%2Fdt+=+K%28be%5E%28-bt%29+-+ae%5E%28-at%29%29