Explanation Given information: The following functions give the populations of four towns with time t in years. P = 600 ( 1.12 ) t P = 1000 ( 1.03 ) t P = 200 ( 1.08 ) t P = 900 ( 0.90 ) 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) P = 600 ( 1.12 ︷ a ) t ⇒ a = 1.12 (ii) P = 1000 ( 1.03 ︷ a ) t ⇒ a = 1.03 (iii) P = 200 ( 1 To determine (b) To find: The town which has the largest initial population and the initial population. To determine (c) To find: Whether any of the towns decreasing in size.

6th Edition

ISBN: 9781119399353

Author: DA

Publisher: JOHN WILEY+SONS,INC.-CONSIGNMENT

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Question

Chapter 1.5, Problem 1P

To determine

(a)

To find:

The town that has the largest percent growth rate and the percent growth rate.

To determine

(b)

To find:

The town which has the largest initial population and the initial population.

To determine

(c)

To find:

Whether any of the towns decreasing in size.

Expert Solution & Answer

Chapter 1 Solutions

EBK APPLIED CALCULUS, ENHANCED ETEXT

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(a) To find: The town that has the largest percent growth rate and the percent growth rate.

Solution Summary: The author explains how the function f(x)=2x gives the population of four towns with time t in years. Exponential growth is often described in terms of percent growth rates.

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(a) To find: The town that has the largest percent growth rate and the percent growth rate.

(b) To find: The town which has the largest initial population and the initial population.

(c) To find: Whether any of the towns decreasing in size.

Chapter 1 Solutions

(a)

To find:

The town that has the largest percent growth rate and the percent growth rate.

(b)

To find:

The town which has the largest initial population and the initial population.

(c)

To find:

Whether any of the towns decreasing in size.