Explanation Method used: Euler’s method: “Consider the differential equation d y d x = F ( x , y ) subject to the initial condition y ( x 0 ) = y 0 . To find an approximation of y ( b ) , where b is a number greater than x 0 and n is a positive integer, compute h = b − x 0 n , x 1 = x 0 + h , x 2 = x 0 + 2 h , x 3 = x 0 + 3 h ... x n = x 0 + n h = b and y 0 = y ( x 0 ) , y 1 = y 0 + h F ( x 0 , y 0 ) , ... , y n = y n − 1 + h F ( x n − 1 , y n − 1 ) . Then y n gives an approximation of the true value y ( b ) of the solution to the initial-value problem at x = b ”. Calculation: From the given information, it is observed that the growth rate of the nonfarm workforce in a certain country is given by the equation as R ( t ) = 5 e 1 ( t + 1 ) . It is given that, the percentage of the nonfarm workforce in the service industries is P ( 1 ) , where P is the solution of P ′ = 5 e 1 ( t + 1 ) with the initial condition P ( 0 ) = 30 . Here, t 0 = 0 , n = 10 and b = 1 . Substitute t 0 = 0 , n = 10 and b = 1 in h = b − t 0 n . h = 1 − 0 10 = 0.1 That is, the value of h is 0.1. Compute the value of t 1 , t 2 , t 3 , t 4 , t 5 , t 6 , t 7 , t 8 , t 9 and t 10 as follows. Substitute t 0 = 0 , and h = 0.1 in t 1 = t 0 + h . t 1 = 0 + 0.1 = 0.1 Substitute t 0 = 0 , and h = 0.1 in t 2 = t 0 + 2 h . t 2 = 0 + 2 ( 0.1 ) = 0.2 Substitute t 0 = 0 , and h = 0.1 in t 3 = t 0 + 3 h . t 3 = 0 + 3 ( 0.1 ) = 0.3 Substitute t 0 = 0 , and h = 0.1 in t 4 = t 0 + 4 h . t 4 = 0 + 4 ( 0.1 ) = 0.4 Substitute t 0 = 0 , and h = 0.1 in t 5 = t 0 + 5 h . t 5 = 0 + 5 ( 0.1 ) = 0.5 Substitute t 0 = 0 , and h = 0.1 in t 6 = t 0 + 6 h . t 6 = 0 + 6 ( 0.1 ) = 0.6 Substitute t 0 = 0 , and h = 0.1 in t 7 = t 0 + 7 h . t 7 = 0 + 7 ( 0.1 ) = 0.7 Substitute t 0 = 0 , and h = 0.1 in t 8 = t 0 + 8 h . t 8 = 0 + 8 ( 0.1 ) = 0.8 Substitute t 0 = 0 , and h = 0.1 in t 9 = t 0 + 9 h . t 9 = 0 + 9 ( 0.1 ) = 0.9 Substitute t 0 = 0 , and h = 0.1 in t 10 = t 0 + 10 h . t 10 = 0 + 10 ( 0.1 ) = 1 Consider the function as F ( t , P ) = 5 e 1 t + 1 , and P ( 0 ) = P 0 = 30 . Compute the value of P 0 , P 1 , P 2 , P 3 , P 4 , P 5 , P 6 , P 7 , P 8 , P 9 and P 10 at the points t 0 , t 1 , t 2 , t 3 , t 4 , t 5 , t 6 , t 7 , t 8 , t 9 and t 10 as listed in the below table

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ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

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Chapter 9.4, Problem 16E

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The percentage of the nonfarm workforce in the service industries.

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Chapter 9 Solutions

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The percentage of the nonfarm workforce in the service industries.

Solution Summary: The author explains how the percentage of the nonfarm workforce in the service industries is underset_40.3772%.

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Chapter 9 Solutions