(d) The secretion of hormones into the blood is often a periodic activity. If a hormone is secreted on a 24h cycle, then the rate of change of the level of the hormone in the blood may be represented by the initial value problem dy -b cos dt (12) - ky, 3(0) = k (e) where y(t) is the amount of the hormone in the blood at time t, a is the average secretion rate, b is the amount of variation in the secretion, and k is a positive constant reflecting the rate at which the body removes the hormone from the blood. Find the solution of the above initial value problem. Consider the solution of the initial value problem in part (d). Find the limiting value of y as t→ ∞ and as t→ 0 and interpret the results.

(d) The secretion of hormones into the blood is often a periodic activity. If a hormone is secreted on a 24h cycle, then the rate of change of the level of the hormone in the blood may be represented by the initial value problem dy -b cos dt (12) - ky, 3(0) = k (e) where y(t) is the amount of the hormone in the blood at time t, a is the average secretion rate, b is the amount of variation in the secretion, and k is a positive constant reflecting the rate at which the body removes the hormone from the blood. Find the solution of the above initial value problem. Consider the solution of the initial value problem in part (d). Find the limiting value of y as t→ ∞ and as t→ 0 and interpret the results.

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section6.8: Fitting Exponential Models To Data

Problem 3TI: Table 6 shows the population, in thousands, of harbor seals in the Wadden Sea over the years 1997 to...

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