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Calculus For The Life Sciences

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter11: Differential Equations

Section11.2: Linear First-order Differential Equations

Problem 12E

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order Bernoul
equation in the
2. The Bernoulli's form of the differential equation 2x³dy-y(y² + 3x²)dx=0 is
3. The Bernoulli's form of the differential equation x³ydx + (3x² - y³)dy = 0 is

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Flea Beetles A study of flea beetles found that the change in the rate of flea beetles moving in and out of a patch of beetles could be described by the differential equation dNdt=mN+i where N is the number of beetles in a patch, m is the rate at which beetles move out of the patch, and i is the rate at which they move in. Source: Ecological Monographs. a. Solve the differential equation above with the initial condition N(0)=N0. b. After the researchers cleared a patch of beetles, so that N0, they would return 8 hours later and count the number of beetles. Show that the parameter i can then be estimated by the equation i=mN(8)e8m1 c. The researchers estimated m using the equation m=lnFsd, where Fsd is the fraction of beetles who remained in the patch in which they were released. For the beetles P, striolata released in July in the lush interior of patches 5 meters apart, the average values of Fsd and N(8) were 0.709 and 4.5, respectively. Find the values of m and i.

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