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Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

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BuyFindarrow_forward

Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Movie Advertising The percentage of movie advertising as a share of newspapers’ total advertising revenue from 1995 to 2004 can be approximated by

p ( t ) = { 0.07 t + 6.0      if  t 4 0.3 t + 17.0      if  t > 4 ,

Where t is time in years since 1995.

a. Compute lim t 4 p ( t )

and lim t 4 + p ( t ) , and interpret each answer. [HINT: See Example 3.]

b. Is the function f continuous at t = 4 ? What does the answer tell you about movie advertising expenditures?

(a)

To determine

To calculate: The limits limt4p(t) and limt4+p(t), if the percentage of movie advertising as a share of newspaper’s total advertising revenue during the period 19952004 is approximated as function of time (t) as p(t)={0.07t+6.0  if t40.3t+17.0     if t>4 and also interpret the answer.

Explanation

Given Information:

The percentage of movie advertising as a share of newspaper’s total advertising revenue during the period 19952004 is approximated as function of time (t) as p(t)={0.07t+6.0  if t40.3t+17.0     if t>4.

Formula used:

Continuity of closed form function theorem:

Every function that is closed is continuous on its domain.

If limxaf(x) exists and f(a) is defined, then

limxaf(x)=f(a)

Calculation:

Consider the function p(t)={0.07t+6.0  if t40.3t+17.0     if t>4.

Consider the right limit:

The closed-form function 0.3t+17.0 exists when t>4.

limt4+p(t)=limt4+(0

(b)

To determine

Whether the function p(t)={0.07t+6.0  if t40.3t+17.0     if t>4 is continuous or not at t=4 and also interpret the answer.

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