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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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The rate of change in sales of Ross Stores from 2004 through 2013 can he modeled by

d S d t = 0.2895 e 0.096 t where S is the sales (in billions of dollars) and t is the time (in years), with t = 4 corresponding to 2004. In 2008, the sales of Ross Stores were $6.5 billion. (Source: Ross Stores, Inc.)

(a) Find a model for the sales of Ross Stores.

(b) What were the average sales of Ross Stores from 2004 through 2013?

(a)

To determine

To calculate: The model for the sales of Ross stores if the rate of change of Ross stores from 2004 to 2013 is given by dSdt=0.2895e0.096t.

Explanation

Given information:

The rate of change of Ross stores from 2004 to 2013 is dSdt=0.2895e0.096t. Where S is the sales in billions of dollars and time is denoted by t. The sales for Ross stores in 2008 were $6.5 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 2004 to 2013 is,

dSdt=0.2895e0.096t.

By the use of antiderivatives rule,

S(t)=0.2895e0.096tdt

Now use basic integration rule,

S(t)=0

(b)

To determine

To calculate: The average sales of Ross stores for 2004 to 2013 if the sales of Ross stores modal obtained from part (a) is S(t)=3.0156e0.096t+0.00002185.

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