Explanation Given: The rate of increase of population is proportional to the number of people present at time t , the initial population has doubled in 5 yeras and the initial population is P 0 . The population after 3 years is 10000 . The time required for the population to quadruple is 10 years . Procedure used: (1) Form a differential equation. (2) Integrate the differential equation. (3) Apply initial conditions. Calculation: Form the differential equation from the given information. d P d t = k P d P P = k d t (1) Here, the population is P , the constant is k and the time is t . Integrate equation (1). ∫ d P P = ∫ k d t ln P = k t + c P = e k t e c (2) Substitute P 0 for P and 0 for t in equation (2). P 0 = e k ⋅ 0 e c P 0 = e c Substitute P 0 for e c in equation (2). P = P 0 e k t (3) Substitute 2 P 0 for P and 5 for t in equation (3). 2 P 0 = P 0 e k ⋅ 5 2 = e k ⋅ 5 5 k = ln 2 k = 1 5 ln 2 Substitute 1 5 ln 2 for k in equation (3). P = P 0 e 1 5 t ln 2 P = P 0 e ln 2 t 5 P = P 0 2 t 5 (4) Substitute 10000 for P and 3 for t in equation (4)

6th Edition

ISBN: 9781284105902

Author: Dennis G. Zill

Publisher: Jones & Bartlett Learning

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Chapter 2.7, Problem 2E

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Determine the population after 10 years and the rate of increase of population.

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1. Name the ongiewing) 2. Name five pairs of supple 3 27 and 19 form a angles 210 and 21 are complementary angies 4. m210=32 mal!= 5 mc11-72 m10= 6 m210-4x mc11=2x x= 7 m210=x m 11 =x+20; x= 12 and 213 are supplementary angles 8 ma 12 2y m13-3y-15 y= 9 m 12-y+10 m13-3y+ 10: y= 10. The measure of 212 is five times the measure of 13. Find the 213 and 214 are complementary angles, and 14 and 15 are supplementary angies 11 mc13 47 m/14- 12 m 14-78 m13- m215- m15 13 m15-135 m. 13- m.14

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