   Chapter 2.3, Problem 56E

Chapter
Section
Textbook Problem

Sales of DVD Players Versus VCRs The sales of DVD players in year t (in millions of units) is given by the functionf(t) = 5.6(1 + t) (0 ≤ t ≤ 3)where t = 0 corresponds to 2001. Over the same period, the sales of VCRs (in millions of units) is given by g ( t ) = { − 9.6 t + 22.5 if  0 ≤ t ≤ 1 − 0.5 t + 13.4 if  1 < t ≤ 2 − 7.8 t + 28 if  2 < t ≤ 3 a. Show that more VCRs than DVD players were sold in 2001. b. When did the sales of DVD players first exceed those of VCRs?

a.

To determine

To show: The sales of VCRs were more than DVDs.

Explanation

Proof:

The sales of DVD players (in millions of units) in year t is,

f(t)=5.6(1+t)(0t3) (1)

Where t=0 corresponds to 2001.

Over the same period, the sales of VCRs (in millions of units) is,

g(t)={9.6t+22.5if0t10.5t+13.4if1<t27

b.

To determine
The time when sales of DVDs were greater than the VCRs.

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