Explanation 1) Concept: Step 1: Compare the given function with the general quadratic function g ( x ) = a x 2 + b x + c Step 2: If a > 1 , the graph of the given function is a parabola that opens upwards. So, it attains minimum value at its vertex. Step 3: If a < 1 , the graph of the given function is a parabola that opens downwards. So, it attains maximum value at its vertex. Step 4: Find the vertex by using the formula ( − b 2 a , f ( − b 2 a ) ) . Step 5: The vertex gives the maximum/minimum value of the function. 2) Calculation: The given function is of f ( x ) = − 0.072 x 2 + 1.93 x + 173.9 On comparison of f ( x ) with the function g ( x ) = a x 2 + b x + c , we find that a = − 0.072 , b = 1.93 and c = 173.9 . Since a < 1 , the graph of the given function is a parabola that opens downward. Therefore, the function attains its maximum at its vertex. To find the x co-ordinate of the vertex, we find − b 2 a . Substitute the values a = − 0.072 and b = 1.93 in − b 2 a . − b 2 a = − 1.93 2 × − 0.072 = − 1.93 − 0.144 = 13.40 Now, we substitute the x co-ordinate of the vertex in the function f ( x ) . That is, we find f ( 13

Pearson eText for Beginning & Intermediate Algebra -- Instant Access (Pearson+)

6th Edition

ISBN: 9780137531929

Author: Elayn Martin-Gay

Publisher: PEARSON+

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Chapter 11.6, Problem 88E

To determine

a) To Answer:

Methane is a gas produced by landfills, natural gas systems, and coal mining that contributes to the greenhouse effect and global warming. Projected methane emissions in the United States can be modeled by the quadratic function f(x)=−0.072x2+1.93x+173.9, where f(x) is the amount of methane produced in million metric tons and x is the number of years after 2000. (Source: Based on data from the U.S. Environmental Protection Agency, 2000-2020)

According to this model, what will U.S. emissions of methane be in 2018? Round to 2 decimal places.

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Chapter 11.6, Problem 87E

Chapter 11.6, Problem 89E

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Chapter 11 Solutions

Pearson eText for Beginning & Intermediate Algebra -- Instant Access (Pearson+)

Ch. 11.1 - Prob. 1G Ch. 11.1 - Prob. 2G Ch. 11.1 - Prob. 3G Ch. 11.1 - Prob. 4G Ch. 11.1 - Prob. 5G Ch. 11.1 - Prob. 6G Ch. 11.1 - Prob. 1P Ch. 11.1 - Prob. 2P Ch. 11.1 - Prob. 3P Ch. 11.1 - Prob. 4P

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