$\"\"$

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(a)

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Find the linear equation of data using regression capabilities.

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Graph the data using regression utility:

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$\"\"$

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Observe the graph:

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The linear model of equation is $\"\"$ .

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$\"\"$

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Find the quadratic equation of data using regression capabilities.

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Graph the data using regression utility:

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$\"\"$

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Observe the graph:

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The quadratic model of equation is $\"\"$ .

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$\"\"$

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(b)

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The linear model of equation is $\"\"$ .

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Compare with the slope-intercept form of line $\"\"$ .

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$\"\"$ .

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The slope in the linear model represents the rate of decline in value over time.

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$\"\"$

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(c)

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Find the exponential equation of data using regression capabilities.

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Graph the data using regression utility:

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$\"\"$

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Observe the graph:

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The exponential model of equation is $\"\"$ .

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$\"\"$

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(d)

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Find the horizontal asymptote of exponential equation.

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The exponential model of equation is $\"\"$ .

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Horizontal asymptotes are horizontal lines that the graph of the function approaches as $\"\"$ tends to $\"\"$ or $\"\"$ .

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The horizontal asymptote is $\"\"$

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$\"\"$

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$\"\"$ .

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The horizontal asymptote is $\"\"$ .

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$\"\"$

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(e)

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Find the rate of decrease in value when $\"\"$ and $\"\"$ using the exponential model.

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The exponential model of equation is $\"\"$ .

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Apply derivative on each side with respect to $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The rate of decrease in value when $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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The rate of decrease in value when $\"\"$ .

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Substitute $\"\"$ in $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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$\"\"$

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(a)

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Graphs:

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The linear model of equation is $\"\"$ .

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$\"\"$

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The quadratic model of equation is $\"\"$ .

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$\"\"$

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(b) The slope in the linear model represents the rate of decline in value over time.

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(c) Graph of the exponential model of equation is $\"\"$ .

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$\"\"$

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The exponential model of equation is $\"\"$ .

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(d) The horizontal asymptote is $\"\"$ .

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(e) $\"\"$ and $\"\"$ .