The average rate of change from 2010 to 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y = 6.97 ( 0.5 x + 5 ) 0.495 where y is the percent and x is the number of years past 2010.

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Answer 1

Question

Chapter 9.6, Problem 54E

(a)

To determine

To calculate: The average rate of change from 2010 to 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010.

(b)

To determine

To calculate: The instantaneous rate of change of the U.S. population with diabetes in 2020. Also, determine if the average rate of change from 2010 to 2050 a good approximation of the 2020 instantaneous rate. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010.

(c)

To determine

To calculate: The instantaneous rate of change of the percent of the U.S. population with diabetes in 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010. Interpret the answer.

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Suppose we have a linear program in standard equation form maximize c'x subject to Ax=b, x≥ 0. and suppose u, v, and w are all optimal solutions to this linear program. (a) Prove that zu+v+w is an optimal solution. (b) If you try to adapt your proof from part (a) to prove that that u+v+w is an optimal solution, say exactly which part(s) of the proof go wrong. (c) If you try to adapt your proof from part (a) to prove that u+v-w is an optimal solution, say exactly which part(s) of the proof go wrong.

(a) For the following linear programme, sketch the feasible region and the direction of the objective function. Use you sketch to find an optimal solution to the program. State the optimal solution and give the objective value for this solution. maximize +22 subject to 1 + 2x2 ≤ 4, 1 +3x2 ≤ 12, x1, x2 ≥0 (b) For the following linear programme, sketch the feasible region and the direction of the objective function. Explain, making reference to your sketch, why this linear programme is unbounded. maximize ₁+%2 subject to -2x1 + x2 ≤ 4, x1 - 2x2 ≤4, x1 + x2 ≥ 7, x1,x20 Give any feasible solution to the linear programme for which the objective value is 40 (you do not need to justify your answer).

find the domain of the function f(x)

Answer 2

Question

Chapter 9.6, Problem 54E

(a)

To determine

To calculate: The average rate of change from 2010 to 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010.

(b)

To determine

To calculate: The instantaneous rate of change of the U.S. population with diabetes in 2020. Also, determine if the average rate of change from 2010 to 2050 a good approximation of the 2020 instantaneous rate. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010.

(c)

To determine

To calculate: The instantaneous rate of change of the percent of the U.S. population with diabetes in 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010. Interpret the answer.

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Answer 3

Question

Chapter 9.6, Problem 54E

(a)

To determine

To calculate: The average rate of change from 2010 to 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010.

(b)

To determine

To calculate: The instantaneous rate of change of the U.S. population with diabetes in 2020. Also, determine if the average rate of change from 2010 to 2050 a good approximation of the 2020 instantaneous rate. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010.

(c)

To determine

To calculate: The instantaneous rate of change of the percent of the U.S. population with diabetes in 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010. Interpret the answer.

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Answer 4

Question

Chapter 9.6, Problem 54E

(a)

To determine

To calculate: The average rate of change from 2010 to 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010.

(b)

To determine

To calculate: The instantaneous rate of change of the U.S. population with diabetes in 2020. Also, determine if the average rate of change from 2010 to 2050 a good approximation of the 2020 instantaneous rate. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010.

(c)

To determine

To calculate: The instantaneous rate of change of the percent of the U.S. population with diabetes in 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010. Interpret the answer.

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Answer 5

Chapter 9.6, Problem 54E

(a)

To determine

To calculate: The average rate of change from 2010 to 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010.

(b)

To determine

To calculate: The instantaneous rate of change of the U.S. population with diabetes in 2020. Also, determine if the average rate of change from 2010 to 2050 a good approximation of the 2020 instantaneous rate. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010.

(c)

To determine

To calculate: The instantaneous rate of change of the percent of the U.S. population with diabetes in 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010. Interpret the answer.

Answer 6

Chapter 9.6, Problem 54E

(a)

To determine

To calculate: The average rate of change from 2010 to 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010.

Answer 7

Chapter 9.6, Problem 54E

(a)

To determine

To calculate: The average rate of change from 2010 to 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010.

Answer 8

(b)

To determine

To calculate: The instantaneous rate of change of the U.S. population with diabetes in 2020. Also, determine if the average rate of change from 2010 to 2050 a good approximation of the 2020 instantaneous rate. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010.

Answer 9

(b)

To determine

To calculate: The instantaneous rate of change of the U.S. population with diabetes in 2020. Also, determine if the average rate of change from 2010 to 2050 a good approximation of the 2020 instantaneous rate. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010.

Answer 10

(c)

To determine

To calculate: The instantaneous rate of change of the percent of the U.S. population with diabetes in 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010. Interpret the answer.

Answer 11

(c)

To determine

To calculate: The instantaneous rate of change of the percent of the U.S. population with diabetes in 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y=6.97(0.5x+5)0.495 where y is the percent and x is the number of years past 2010. Interpret the answer.

Answer 12

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Answer 13

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Answer 14

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Answer 15

Ch. 9.1 - 1. Can exist if is undefined? Ch. 9.1 - 2. Does exist if ? Ch. 9.1 - 3. Does Ch. 9.1 - 4. If , does exist? Ch. 9.1 - 5. Let (a) Does (b) Find . Ch. 9.1 - 6. Evaluate the following limits (if they...Ch. 9.1 - Prob. 7CP Ch. 9.1 - Prob. 8CP Ch. 9.1 - Prob. 9CP Ch. 9.1 - Prob. 10CP

The average rate of change from 2010 to 2050. The figure shows the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050. Assume that this percent can be modeled by y = 6.97 ( 0.5 x + 5 ) 0.495 where y is the percent and x is the number of years past 2010.

Solution Summary: The author calculates the percent of the U.S. population with diabetes for selected years from 2010 and projections to 2050.

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