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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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Consumer Trends For the years 2003 through 2012, the per capita consumption C of all fruit (in pounds) in the United States can be modeled by

{ 0.59 t 2 3.69 t + 293.3 t 9 3.245 t 2 + 65.475 t 73.67 , 9 < t 12 where / is the year, with t = 3 corresponding to 2003. (Source: U.S. Department of Agriculture)

(a) Use a graphing utility to graph this model.

(b) Suppose the fruit consumption from 2010 through 2012 had continued to follow the model for 2003 through 2009. How many more or fewer pounds of fruit would have been consumed from 2010 through 2012?

(a)

To determine

To graph: The function that models the per Capita consumption C of all fruit (in pounds) in the United States for the years 2003 through 2012.

C(t)={0.059t2   3.69t+293.6,   3t93.245t2+65.475t73.67,  9<t12

Explanation

Given Information:

The function that models the per Capita consumption C of all fruit (in pounds) in the United States for the years 2003 through 2012.

C(t)={0.059t2   3.69t+293.6,   3t93.245t2+65.475t73.67,  9<t12

Here, t is the year and t=3 corresponding to 2003.

Graph:

Use Ti-83 calculator to graph the provided region as follows:

Step 1: Press "Y=" key. Insert the given piecewise function as two functions

Y1=0.059X23.69X+293.6

And

Y2=3.245X2+65.475X73.67

Step 2: Press “Window” key

(b)

To determine

To calculate: How many more of fewer pounds of fruits would have been consumed from 2010 through 2012 if fruit consumption had continued to follow the model C2(t)=0.059t23.69t+293.6 in place of the model C1(t)=3.245t2+65.475t73.67.

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