Given the exponential growth function Pr = 77(1.0315)” What is the initial value, Po, of the function? What is the growth factor, or growth rate of the function (as a percent)? % Question Help: Read

Given the exponential growth function Pr = 77(1.0315)” What is the initial value, Po, of the function? What is the growth factor, or growth rate of the function (as a percent)? % Question Help: Read

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter4: Exponential Functions

Section4.1: Exponential Growth And Decay

Problem 16SBE: Exponential Growth Is the graph of exponential growth versus time increasing or decreasing?

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Question

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Given the exponential growth function P₁ = 77(1.0315)"
What is the initial value, Po, of the function?
What is the growth factor, or growth rate of the function (as a percent)?
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In this exercise, we consider data from the Statistical Abstract of the United States on the fraction of women married for the first time in 1960 whose marriage reached a given anniversary number. The data show that the fraction of women who reached their fifth anniversary was 0.928. After that, for each one-year increase in the anniversary number, the fraction reaching that number drops by about 2%. These data describe constant percentage change, so it is reasonable to model the fraction M as an exponential function of the number n of anniversaries since the fifth. (a) What is the yearly decay factor for the exponential model?(b) Find an exponential model for M as a function of n. (Let n = 0 represent the fifth anniversary.) M = (c) According to your model, what fraction of women married for the first time in 1960 celebrated their 50th anniversary? (Take n = 45.) Round your answer to three decimal places.
In this exercise, we consider data from the Statistical Abstract of the United States on the fraction of women married for the first time in 1960 whose marriage reached a given anniversary number. The data show that the fraction of women who reached their fifth anniversary was 0.928. After that, for each one-year increase in the anniversary number, the fraction reaching that number drops by about 2%. These data describe constant percentage change, so it is reasonable to model the fraction M as an exponential function of the number n of anniversaries since the fifth.