   Chapter 6.1, Problem 63E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Demand A manufacturing company forecasts that the demand x (in units) for its product over the next 10 years can be modeled by x   =   500 ( 20   +     t e − 0.1 t ) , 0 ≤ t ≤ 10 where t is the time in years.(a) Use a graphing utility to decide whether the company is forecasting an increase or a decrease in demand over the decade.(b) Find the total demand over the next 10 years.(c) Find the average annual demand during the 10-year period.

(a)

To determine

Whether company is forecasting an increase or decrease in the demand over the decade by using graphing utility when a manufacturing company forecast the demand x (in units) for it’s product over the next 10 years is modeled by the function,

x=500(20+te0.1t),   0t10

Where t is the time in years.

Explanation

Given Information:

A manufacturing company forecast the demand x (in units) for it’s product over the next 10 years is modeled by the function,

x=500(20+te0.1t),   0t10

Where t is the time in years.

Consider the function,

x=500(20+te0.1t),   0t10 .

Now use TI-83 graphing calculator to obtain the graph by following the provided steps as,

Step 1: Press the [WINDOW] key and set the window as,

Xmin=0Xmax=10X scl=2Ymin</

(b)

To determine

To calculate: The total demand over the next 10 years when a manufacturing company forecast the demand x (in units) for it’s product over the next 10 years is modeled by the function,

x=500(20+te0.1t),   0t10

Where t is the time in years.

(c)

To determine

To calculate: The average annual demand over the period of 10 years when a manufacturing company forecast the demand x (in units) for it’s product over the next 10 years which is modeled by the function,

x=500(20+te0.1t),   0t10

Where t is the time in years.

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