Repeat Exercise 7, but in place of f(t) put a * e (p * t), the

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Repeat Exercise 7, but in place of f(t) put a * e Λ (–p * t), the form of PL(t) used in Exercises 5. Verify that the solution is equivalent to the solution given in Exercise 6.


Data from Exercises 7

At the website Wolfram Alpha.com, you can enter “y´(t) = (f(t) – y) * k, y(0) = a ” to solve the initial value problem in this Extended Application, where we have used y(t) to represent PL(t), f(t) to represent Pi(t), and a to represent PL(0) Try this, and verify that the solution is equivalent to Equation (1).


Equation 1


Data from Exercises 5

Suppose that instead of assuming that all pollution inflow immediately ceases, we model Pi(t) by a decaying exponential of the form a · e–pt where p is a constant that tells us how fast the inflow is being cleaned of pollution. To simplify things, we’ll also assume that initially the inflow and the lake have the same pollution concentration, so a = PL(0)Now substitute a = PL(0)e–px for Pi(x) in Equation (1), and evaluate the integral as a function of t

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Calculus With Applications

ISBN: 9780321831101

10th Edition

Authors: Margaret L Lial, Raymond N Greenwell, Nathan P Ritchey

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