Chapter 5, Problem 86RE

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

10th Edition
Ron Larson
ISBN: 9781305860919

Chapter
Section

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

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Sales The rate of change in sales for Garmin from 2008 through 2013 can be modeled by d S d t =   − 0.0972 t 2 +   2.146 t   −   11.79 where S is the sales (in billions of dollars) and t is the time in years, with t = 8 corresponding to 2008. In 2009, the sales for Garmin were $2.9 billion. (Source: Garmin, Ltd.)(a) Find the model for the sales of Garmin.(b) What were the average sales of Garmin from 2008 through 2013? (a) To determine To calculate: The model for the Garmin sales if the rate of change of Garmin sale from 2008 to 2013 is given by dSdt=0.0972t2+2.146t11.79. Explanation Given information: The rate of change of Garmin sale from 2008 to 2013 is dSdt=0.0972t2+2.146t11.79. Where S is the sales in billions of dollars and time is denoted by t. The sales for Garmin in 2009 were$2.9 billion.

Formula used:

The integration formula,

xndx=xn+1n+1+c

Where n1

Antiderivatives rule,

f(x)dx=f(x)+c

Calculation:

Consider the rate of change from 2008 to 2013 is,

dSdt=0.0972t2+2.146t11.79.

Use antiderivatives rule,

S(t)=(0.0972t2+2.146t11.79)dt

Now use Basic integration formula,

S(t)=0.0972t2+2.146t11.79=0

(b)

To determine

To calculate: The average sales of Garmin for 2008 to 2013 if the sales of Garmin modal obtained from part (a) is S(t)=0.0324t3+1.073t211.79t+45.72.

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