/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 14 Give the growth rate that corres... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 10: Problem 14

Give the growth rate that corresponds to the given growth factor. 0.639

Short Answer

Expert verified
Answer: The growth rate corresponding to a growth factor of 0.639 is -36.1%.

Step by step solution

01

Write down the formula for calculating the growth rate from growth factor

Growth Rate = (Growth Factor - 1) * 100
02

Plug in the given growth factor value

Growth Rate = (0.639 - 1) * 100
03

Perform the calculation

Growth Rate = (-0.361) * 100
04

Find the final growth rate

Growth Rate = -36.1% The growth rate that corresponds to the given growth factor of 0.639 is -36.1%.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Growth Factor
The growth factor is a number that tells us how much something has grown or shrunk compared to its original size. If the growth factor is greater than 1, it means growth. If it's less than 1, there is shrinkage or decrease.
For example, a growth factor of 0.639 indicates that the original value has decreased to 63.9% of what it was. Understanding this concept helps in calculating the growth rate and predicting future trends.
Percentage Change
Percentage change is a way to express how much a quantity has increased or decreased in percentage terms. It is calculated using the growth factor.
  • If the growth factor is less than 1, the percentage change will be negative, showing a decrease.
  • If the growth factor is more than 1, the percentage will be positive, meaning an increase.

In the given example, converting the growth factor 0.639 to a percentage change involves using the formula: \( (0.639 - 1) \times 100 \) which equals -36.1%.
This negative result confirms a decrease.
Negative Growth
Negative growth indicates a decline or reduction in value. This is seen when the growth factor is less than 1, or the percentage change is negative. For example, in economics, this might signify that a country's economy has contracted.
In our exercise, the negative growth rate of -36.1% means a 36.1% reduction in the original value. Understanding negative growth is crucial for financial analysis, budgeting, and planning.
Mathematical Formula
Mathematical formulas provide the steps needed to solve problems by plugging in values. The formula to calculate growth rate from a growth factor is \( \text{Growth Rate} = (\text{Growth Factor} - 1) \times 100 \).
This formula helps convert a growth factor into a more understandable growth rate or percentage change.
By applying the growth factor of 0.639 to the formula, we calculate the growth rate as -36.1%.
  • This shows the importance of formulas in breaking down problems into manageable parts.
  • They are essential tools for analysis and decision-making across various fields.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

You buy a house for \(\$ 350,000\), and its value declines at a continuous rate of \(-9 \%\) a year. What is it worth after 5 years?

Solve the equations in Problem using the following approximations: $$ 10^{0.301}=2, \quad 10^{0.477}=3, \quad 10^{0.699}=5 . $$ Example. Solve \(10^{x}=6 .\) Solution. We have $$ \begin{aligned} 10^{x} &=6 \\ &=2 \cdot 3 \\ &=10^{0.301} \cdot 10^{0.477} \\ &=10^{0.301+0.477} \\ &=10^{0.778} \\ \text { so } x=0.778 . \end{aligned} $$ \(10^{x}=15\)

Match each statement (a)-(b) with the solutions to one or more of the equations (I)-(VI). I. \(10(1.2)^{t}=5\) II. \(10=5(1.2)^{t}\) III. \(10+5(1.2)^{t}=0\) IV. \(5+10(1.2)^{t}=0\) V. \(10(0.8)^{t}=5\) VI. \(5(0.8)^{t}=10\) (a) The time an exponentially growing quantity takes to grow from 5 to 10 grams. (b) The time an exponentially decaying quantity takes to dron from 10 to 5 grams

Find possible formulas for the exponential functions described. An investment initially worth \(\$ 3000\) grows by \(30 \%\) over a 5-year period.

From Figure \(10.6,\) when is (a) \(100(1.05)^{t}>121.55 ?\) (b) \(100(1.05)^{t}<121.55 ?\)
See all solutions

Recommended explanations on Math Textbooks

Decision Maths

Read Explanation

Applied Mathematics

Read Explanation

Logic and Functions

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.