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7. The field mouse population in Example 1 satisfies the differential equation dy P dt 2 = - 450. a. Find the time at which the population becomes extinct if p(0) = 850. b. Find the time of extinction if p(0) = Po, where 0 < Po < 900. Nc. Find the initial population po if the population is to become extinct in 1 year.

7. The field mouse population in Example 1 satisfies the differential equation dy P dt 2 = - 450. a. Find the time at which the population becomes extinct if p(0) = 850. b. Find the time of extinction if p(0) = Po, where 0 < Po < 900. Nc. Find the initial population po if the population is to become extinct in 1 year.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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e y e :) 2) also differ only by a constant. Test this assumption by trying to find a constant k such that y = y(t) + k is a solution of equation (31). c. Compare your solution from part b with the solution given in the text in equation (17). Note: This method can also be used in some cases in which the constant b is replaced by a function g(t). It depends on whether you can guess the general form that the solution is likely to take. This method is described in detail in Section 3.5 in connection with second- order equations. 20 sed 6. Use the method of Problem 5 to solve the equation 7. The field mouse differential equation dy = -ay+b. dt population in Example 1 satisfies the dy P dt 2 - 450. a. Find the time at which the population becomes extinct if p(0) = 850. b. Find the time of extinction if p(0) = Po, where 0 < Po < 900. N c. Find the initial population po if the population is to become extinct in 1 year. 8. The falling object in Example 2 satisfies the initial value problem dv dt a. Find the time that must elapse for the object to reach 98% of its limiting velocity. b. How far does the object fall in the time found in part a? = 9.8 5' V(0) = 0.
Transcribed Image Text:e y e :) 2) also differ only by a constant. Test this assumption by trying to find a constant k such that y = y(t) + k is a solution of equation (31). c. Compare your solution from part b with the solution given in the text in equation (17). Note: This method can also be used in some cases in which the constant b is replaced by a function g(t). It depends on whether you can guess the general form that the solution is likely to take. This method is described in detail in Section 3.5 in connection with second- order equations. 20 sed 6. Use the method of Problem 5 to solve the equation 7. The field mouse differential equation dy = -ay+b. dt population in Example 1 satisfies the dy P dt 2 - 450. a. Find the time at which the population becomes extinct if p(0) = 850. b. Find the time of extinction if p(0) = Po, where 0 < Po < 900. N c. Find the initial population po if the population is to become extinct in 1 year. 8. The falling object in Example 2 satisfies the initial value problem dv dt a. Find the time that must elapse for the object to reach 98% of its limiting velocity. b. How far does the object fall in the time found in part a? = 9.8 5' V(0) = 0.
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