(a) Explanation Given Information: Annual spending on Medicare was projected to increase from $526 billion in 2010 to around $977 billion in 2021. Formula used: The formula for the linear function is y = f ( t ) = p + q t , where p represents the value when t = 0 , and q is called the slope of y and gives the rate of change of y . The equation of a line passing through two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 ) . Calculation: Consider the problem, Annual spending on Medicare was projected to increase from $526 billion in 2010 to around $977 billion in 2021. Since, t represents the number of years since 2010. Let t = 0 represents the year 2010. Then, t = 11 represents the year 2021, At t = 0 , the annual spending on Medicare was $526 billion and at t = 11 , the annual spending on Medicare will be around $977 billion. Therefore, the points are ( t , s ) = ( 0 , 526 ) and ( 11 , 977 ) . Recall that, the equation of a line passing through two points ( x 1 , y 1 ) and ( x 2 , y 2 ) is y − y 1 = y 2 − y 1 x 2 − x 1 ( x − x 1 ) (b) To determine To calculate: The 4-year moving average of s ( t ) = 41 t + 526 . (c) To determine What can be said about the slope of moving average s ¯ ( t ) = 41 t + 444 of the function s ( t ) = 41 t + 526 .

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Chapter 7.3, Problem 55E

(a)

To determine

To calculate: A linear function of t, the number of years since 2010, expressed by s, the annual spending of Medicare (in billions of dollars). Annual spending on Medicare was projected to increase from $526 billion in 2010 to around $977 billion in 2021.

(b)

To determine

To calculate: The 4-year moving average of s(t)=41t+526.

(c)

To determine

What can be said about the slope of moving average s¯(t)=41t+444 of the function s(t)=41t+526.

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Chapter 7.3, Problem 54E

Chapter 7.3, Problem 56E

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Chapter 7 Solutions

Applied Calculus, Loose-leaf Version

Ch. 7.1 - In Exercises 140, evaluate the integral using...Ch. 7.1 - In Exercises 140, evaluate the integral using...Ch. 7.1 - In Exercises 140, evaluate the integral using...Ch. 7.1 - Prob. 4E Ch. 7.1 - Prob. 5E Ch. 7.1 - In Exercises 140, evaluate the integral using...Ch. 7.1 - Prob. 7E Ch. 7.1 - Prob. 8E Ch. 7.1 - In Exercises 140, evaluate the integral using...Ch. 7.1 - In Exercises 140, evaluate the integral using...

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A linear function of t , the number of years since 2010, expressed by s , the annual spending of Medicare (in billions of dollars). Annual spending on Medicare was projected to increase from $526 billion in 2010 to around $977 billion in 2021.

Solution Summary: The author calculates a linear function of t, the number of years since 2010, expressed by s, and the annual spending of Medicare.

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To calculate: A linear function of t, the number of years since 2010, expressed by s, the annual spending of Medicare (in billions of dollars). Annual spending on Medicare was projected to increase from $526 billion in 2010 to around $977 billion in 2021.

To calculate: The 4-year moving average of s(t)=41t+526.

What can be said about the slope of moving average s¯(t)=41t+444 of the function s(t)=41t+526.

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