4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 3.5, Problem 44E

a .

To determine

To estimate: sales in 2020 using the given graph.

a .

Expert Solution

Answer to Problem 44E

40000 units

Explanation of Solution

Given:

The sales began to drop according to the model

S=500,0001+0.1ekt.........(1)

Where S represents the number of units sold and t represents the year, with t=0 corresponding to 2010.

The graph representing this model is:

EBK PRECALCULUS W/LIMITS, Chapter 3.5, Problem 44E , additional homework tip 1

It is given that t=0 corresponding to 2010, so t=10 corresponds to the year 2020.

Now, it the given graph, draw the line t=10 and at the point where it intersects the graph, draw a line parallel to x axis passing through this point.

The point where this line intersects the y-axis gives the number of units sold in the year 2020.

EBK PRECALCULUS W/LIMITS, Chapter 3.5, Problem 44E , additional homework tip 2

By looking at the graph it can be estimated that the sales of the year 2020 are nearly 40,000.

To determine

To find: the value of k.

Expert Solution

Answer to Problem 44E

k=0.4743

Explanation of Solution

Given:

The sales began to drop according to the model

S=500,0001+0.1ekt.........(1)

Where S represents the number of units sold and t represents the year, with t=0 corresponding to 2010.

Also in the year 2014, sales were 300,000.

Formula used:

lnex=x

The year 2014 corresponds to t=4 .

The given population model gives the population in thousands Substitute S=300,000 and t=4 in equation (1), to find value of k.

300,000=500,0001+0.1e4k1+0.1e4k=5000003000001+0.1e4k=53

0.1e4k=53−10.1e4k=23e4k=23×0.1e4k=203

Take natural logarithms on both sides,

lne4k=ln2034k=ln203k=14ln203k≈0.4743

Substituting k=0.4743 in equation (1), the sales are given by,

S=500,0001+0.1e0.4743t

To determine

To estimate: sales in 2020 using the model.

Expert Solution

Answer to Problem 44E

40,071units

Explanation of Solution

Given:

The sales began to drop according to the model

S=500,0001+0.1e0.4743t.........(2)

Where S represents the number of units sold and t represents the year, with t=0 corresponding to 2010.

It is given that t=0 corresponding to 2010, so t=10 corresponds to the year 2020.

So, substitute t=10 in equation (2),

S=500,0001+0.1e0.4743(10)≈40,071.16

Thus, sales is 2020 are nearly 40,071 units.

The sales in 2020 as obtained from part (a) are 40,000.

So, comparing the two, it can be said that both part (a) and part (c) provides nearly the same result.

Chapter 3.5, Problem 43E

Chapter 3.5, Problem 45E

Chapter 3 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E

Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 34E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - Prob. 54E Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - Prob. 60E Ch. 3.1 - 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