Explanation Given information: In the 1990s, Brazil had a deforestation rate of about 0.485 per year. This is the rate at which land covered by forests in shrinking. Concept Involved: The function f ( x ) = 2 x , where the power is variable, is an exponential function. The number is called the base. Exponential functions of the form f ( x ) = k ⋅ a x , where a is a positive constant, are used to represent many phenomena in the natural and social sciences. The General Exponential Function: Exponential decay is often described in terms of percent decay rates. We say that P is an exponential function of t with base a if P = P 0 a t , where P 0 is the initial quantity (when t = 0 ) and a is the factor by which P changes when t increases by 1. If a>1, we have exponential growth; if 0 < a < 1 , we have exponential decay. The factor a is given by a = 1 + r where r is the decimal representation of the percent rate of change; r may be positive (for growth) or negative (for decay). Calculation: Steps Description A 0 = 100 A ( t ) = 100 ⋅ a t A(t) is anexponential function of the form A ( t ) = A 0 ︷ I n i t i a l A r e a ⋅ a ︸ d e c a y f a c t o r t . Since the initial area of forest in 1990 is not provided, let us assume A 0 = 100 a = 1 + r r = − 0.48 % = − 0.48 100 = − 0.0048 a = 1 − 0

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 1.5, Problem 17P

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The percent of the land in Brazil covered by forest in 1990 will be forested in 2030.

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Chapter 1.5, Problem 16P

Chapter 1.5, Problem 18P

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APPLIED CALCULUS (WILEY PLUS)

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The percent of the land in Brazil covered by forest in 1990 will be forested in 2030.

Solution Summary: The author explains that Brazil had a deforestation rate of about 0.485 per year. Exponential functions of the form f(x)=kcdot ax

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To find: The percent of the land in Brazil covered by forest in 1990 will be forested in 2030.

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The percent of the land in Brazil covered by forest in 1990 will be forested in 2030.