Explanation Given information: The given function is N ( x ) = 500 ( 400 + 20 x ) 1 2 ( 5 + 0.2 x ) 2 . Where, N ( x ) is the number of serious crime in certain area. x is the level of reinvestment in the area. Formula used: The formula to calculate the differential of a function h ( x ) = [ g ( x ) ] n by General Power Rule is, h ′ ( x ) = n [ g ( x ) ] n − 1 g ′ ( x ) The formula to calculate the differential of a function h ( x ) = g [ f ( x ) ] by Chain Rule is, d d x g [ f ( x ) ] = g ' [ f ( x ) ] ⋅ f ' ( x ) Calculation: Change in value of x is, d x = 22 − 20 = 2 Differentiate the function N ( x ) = 500 ( 400 + 20 x ) 1 2 ( 5 + 0.2 x ) 2 with respect to t on both sides. d d x ⋅ N ( x ) = d d x ( 500 ( 400 + 20 x ) 1 2 ( 5 + 0.2 x ) 2 ) ⋅ ( d x ) = 500 [ ( 5 + 0.2 x ) 2 ⋅ 10 400 + 20 x − 400 + 20 x ⋅ ( 2 ) ⋅ ( 5 + 0.2 x ) ⋅ ( 0

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ISBN: 9781337825597

Author: Tan

Publisher: INTER CENG

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Chapter 3.7, Problem 45E

To determine

To find: The approximate change in the number of crimes if the level of reinvestment changes from 20 dollar deposited to 22 dollar deposited.

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Chapter 3 Solutions

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Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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The approximate change in the number of crimes if the level of reinvestment changes from 20 dollar deposited to 22 dollar deposited.

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To find: The approximate change in the number of crimes if the level of reinvestment changes from 20 dollar deposited to 22 dollar deposited.

Chapter 3 Solutions