Chapter 9: Chapter 9

Problem 104

\(\nabla\) Describe a real-life situation in which a quadratic model would be more appropriate than an exponential model and one in which an exponential model would be more appropriate than a quadratic model.

Short Answer

Expert verified

A quadratic model is more appropriate for modeling the trajectory of a projectile, as its parabolic shape represents the object's motion affected by gravity, initial velocity, and constant acceleration. The equation is \(y(x) = ax^2 + bx + c\). An exponential model is more suitable for population growth, such as bacteria, where the population increases rapidly with each generation. The equation is \(y(x) = A \cdot b^x\), where A is the initial population and b is the growth factor.

See the step by step solution

Step by step solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Quadratic Model Situation

A real-life situation where a quadratic model would be more appropriate than an exponential model is the trajectory of a projectile. When an object is thrown or launched, its motion can be modeled using a quadratic equation, with the height (y) being a function of time (x). The equation usually takes the form: \(y(x) = ax^2 + bx + c\) where a, b, and c are constants. The parabolic shape of a quadratic model is ideal for representing the projectile's motion as it represents the object's initial position, the combined effect of gravity and the object's initial velocity, and the constant acceleration due to gravity.

Step 2: Exponential Model Situation

A real-life situation where an exponential model would be more appropriate than a quadratic model is population growth. Populations of certain species (for example bacteria) often grow exponentially, with the number of individuals (y) as a function of time (x). The equation usually takes the form: \(y(x) = A \cdot b^x\) where A is the initial population and b represents the growth factor. Exponential growth models can capture the continuous increase in population with each generation due to rapid reproduction. This type of behaviour cannot be accurately represented using a quadratic model as the population would eventually reach its maximum and start decreasing, which is not the case in many population growth scenarios.

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Recommended explanations on Math Textbooks

Find Study Materials for

Create Study Materials

Select your language

Chapter 9: Chapter 9

\(\nabla\) Describe a real-life situation in which a quadratic model would be more appropriate than an exponential model and one in which an exponential model would be more appropriate than a quadratic model.

Short Answer

Step by step solution

Unlock all solutions

Step 1: Quadratic Model Situation

Step 2: Exponential Model Situation

Access millions of textbook solutions in one place

Most popular questions from this chapter

More chapters from the book ‘Finite Mathematics and Applied Calculus’

Chapter 0

Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 15

Chapter 16

Join over 22 million students in learning with our Vaia App

Recommended explanations on Math Textbooks

Statistics

Geometry

Probability and Statistics

Decision Maths

Pure Maths

Mechanics Maths