?The family of functions ????(????) ? ????(????-???????? ? ????-????????), where ????

Chapter 4, Problem 36

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The family of functions 𝑓(𝑡) = 𝐶(𝑒-𝑎𝑡 − 𝑒-𝑏𝑡), where 𝑎, 𝑏, and 𝐶 are positive numbers and 𝑏 > 𝑎, has been used to model the concentration of a drug injected into the bloodstream at time 𝑡 = 0. Graph several members of this family. What do they have in common? For fixed values of 𝐶 and 𝑎, discover graphically what happens as 𝑏 increases. Then use calculus to prove what you have discovered.

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