Explanation Given information: The consumer price index (CPI) for a given year is the amount of money in that year that has the same purchasing power as $100 in 1983. At the start of 2015, the CPI was 234, and the CPI increases by 1.85 every year. 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 P 0 = $ 234 P ( t ) = 234 ⋅ a t P(t) is anexponential function of the form P

6th Edition

ISBN: 9781119399322

Author: Hughes-Hallett

Publisher: WILEY

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Chapter 1.5, Problem 16P

To determine

To find:

A formula for the CPI as a function of t years after 2015, assuming that the CPI increases by 1.8% every year.

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Chapter 1.5, Problem 15P

Chapter 1.5, Problem 17P

Chapter 1 Solutions

APPLIED CALCULUS (WILEY PLUS)

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A formula for the CPI as a function of t years after 2015, assuming that the CPI increases by 1.8% every year.

Solution Summary: The author describes the CPI as a function of t years after 2015, assuming that it increases by 1.8% every year. Exponential decay is often described in terms of percent decay rates.

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To find: A formula for the CPI as a function of t years after 2015, assuming that the CPI increases by 1.8% every year.

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Chapter 1 Solutions

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A formula for the CPI as a function of t years after 2015, assuming that the CPI increases by 1.8% every year.