Explanation Given information: Figure 1.71 shows four different exponential functions Q = 50 ( 1.2 ) t , Q = 50 ( 0.6 ) t , Q = 50 ( 0.8 ) t and Q = 50 ( 1.4 ) t Concept Used: 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 growth is often described in terms of percent growth 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 (i) Q = 50 ( 1.4 ︷ a ) t ⇒ a = 1.4 (ii) Q = 50 ( 1.2 ︷ a ) t ⇒ a = 1.2 (iii) Q = 50 ( 0.8 ︷ a ) t ⇒ a = 0.8 (iv) Q = 50 ( 0

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Chapter 1.5, Problem 3P

To determine

To find:

The initial amount (at t = 0), state whether the function represents exponential growth or decay, and give the percent growth or decay rate.

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Chapter 1.5, Problem 2P

Chapter 1.5, Problem 4P

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Chapter 1 Solutions

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The initial amount (at t = 0), state whether the function represents exponential growth or decay, and give the percent growth or decay rate.

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To find: The initial amount (at t = 0), state whether the function represents exponential growth or decay, and give the percent growth or decay rate.

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The initial amount (at t = 0), state whether the function represents exponential growth or decay, and give the percent growth or decay rate.