A diabetic patient receives insulin at constant rate from an implanted insulin pump. Insulin has first order elimination kinetics, so the amount of insulin in the blood will obey the given differential equation, where a> 0 is the rate at which insulin is released into their blood by the pump and k, is the fraction of insulin removed from the blood in one unit of time. dM dt = a - k,M (a) Assuming M(0) = 0 (i.e., there is no insulin present in the patient's blood at time t = 0), solve the differential equation to find M(t) as a function of t. (b) Find the limit of M(t) as t→o. (c) Assume that a (the rate of release from the pump) is 5 IU/hr and M(t) → 0.2 IU as t→o0. Calculate k1, the rate of insulin elimination. (a) M(t) = U %3D (b) lim→M(t) = 00 (c) k, = | (Type an integer or decimal rounded to three decimal places as needed.) %3D

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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.