After injection of a dose $D$ of insulin, the concentration of insulin in a patient's system decays exponentially and so it can be written as $D e^{-a t},$ where $t$ represents time in hours and $a$ is a positive constant.(a) If a dose $D$ is injected every $T$ hours, write an expression for the sum of the residual concentrations just before the $(n+1)$ st injection.(b) Determine the limiting pre-injection concentration.(c) If the concentration of insulin must always remain at or above a critical value $C,$ determine a minimal dosage $D$ in terms of $C, a,$ and $T$

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
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Chapter6: Vector Spaces
Section6.7: Applications
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After injection of a dose $D$ of insulin, the concentration of insulin in a patient's system decays exponentially and so it can be written as $D e^{-a t},$ where $t$ represents time in hours and $a$ is a positive constant.
(a) If a dose $D$ is injected every $T$ hours, write an expression for the sum of the residual concentrations just before the $(n+1)$ st injection.
(b) Determine the limiting pre-injection concentration.
(c) If the concentration of insulin must always remain at or above a critical value $C,$ determine a minimal dosage $D$ in terms of $C, a,$ and $T$

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