BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

15th Edition

ISBN: 9781608408405

Author: HOUGHTON MIFFLIN HARCOURT

Publisher: Cengage Learning

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

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Question

Chapter 6.7, Problem 30E

To determine

To create:A scatter plot of the points $(x, lny)$ to determine whether an exponential model fits the data, if so , find an exponential model for the data.

Expert Solution & Answer

Answer to Problem 30E

The exponential function that models the data is $y=1.18(3.9)x$ .

Explanation of Solution

Given information:

The given data is $x−8−5−214y1.41.675.326.417.97$ .

Calculation :

Create a table of data pairs $(x, lny)$ .

$x−8−5−214lny0.340.511.671.862.08$

Plot the above transformed points as shown below:

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015, Chapter 6.7, Problem 30E

Since, the point lie close to a line, so an exponential model should be a good fit for the original data.

Find an exponential model $y=abx$ by choosing any two points on the line, such as $(−5, 0.51)$ and $(4, 2.08)$ . Use these points to write an equation of the line. Then solve for y.

Therefore,

$lny−0.51=2.08−0.514+5(x+5) (Equation of the line)lny−0.51=0.17(x+5) (Simplify) lny=0.17x+1.36 y=e0.17x+1.36 (Exponentiate each side using base e)y=e0.17x(e1.36) (Use peoperty of exponents)y=1.18(3.9)x (Simplify)$

Hence,

The exponential function that models the data is $y=1.18(3.9)x$ .

Chapter 6.7, Problem 29E

Chapter 6.7, Problem 31E

Chapter 6 Solutions

BIG IDEAS MATH Algebra 2: Common Core Student Edition 2015

Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Prob. 13E Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - Prob. 55E Ch. 6.1 - Prob. 56E Ch. 6.1 - Prob. 57E Ch. 6.1 - Prob. 58E Ch. 6.1 - Prob. 59E Ch. 6.1 - Prob. 60E Ch. 6.2 - 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To create :A scatter plot of the points ( x , ln y ) to determine whether an exponential model fits the data, if so , find an exponential model for the data.

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Answer to Problem 30E

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Chapter 6 Solutions