Wind Turbine Noise Level Analysis
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Questions and Answers

What is the value of the constant a in the noise level function S(d) when d = 0?

  • 0
  • 105 (correct)
  • 100
  • 49

    • What is the approximate value of b in the function S(d) modeled by S(d) = abd?

  • 0.992408 (correct)
  • 2.0
  • 1.1
  • 0.5

    • What is the average rate of change of the noise level from d = 0 to d = 100 meters?

  • 1.1 decibels per meter
  • -1.0 decibels per meter
  • -0.56 decibels per meter (correct)
  • 0.5 decibels per meter

    • If the average rate of change is -0.56 decibels per meter, what would the estimated noise level be at d = 120 meters?

    <p>37.8 decibels</p> Signup and view all the answers

    What equation must be solved to find the distance m where the noise level is 20 decibels?

    <p>20 = 105(0.992408)<sup>m</sup></p> Signup and view all the answers

    What is the value of (g o h)(2)?

    <p>3</p> Signup and view all the answers

    What does a negative average rate of change indicate in the context of noise level from the turbine?

    <p>Noise level is decreasing with distance</p> Signup and view all the answers

    If the noise level at d = 100 meters is 49 decibels, what is the sound level at this distance compared to d = 0 meters?

    <p>It has decreased significantly</p> Signup and view all the answers

    Which of the following represents the expression for j(h(x)) simplified?

    <p>-4x^2 + 20x - 24</p> Signup and view all the answers

    Considering the noise level function S(d) = 105(0.992408)d, what happens to the noise level as d increases?

    <p>Noise level decreases gradually</p> Signup and view all the answers

    What is the inverse function f-1(x) when f(x) = (x - 4)2 + 3?

    <p>√(x - 3) + 4</p> Signup and view all the answers

    For what values of x does f-1(f(x)) = x hold true?

    <p>x ≥ 3</p> Signup and view all the answers

    What is the equation of the exponential function that goes through the points (1, 8) and (2, 4)?

    <p>f(x) = 16(1/2)<sup>x</sup></p> Signup and view all the answers

    What is the value of x that satisfies the equation 9-x+15 = 27x?

    <p>6</p> Signup and view all the answers

    What value of 'a' results in the graph of f o g crossing the y-axis at 23?

    <p>3</p> Signup and view all the answers

    What is the correct simplified form of (j o h)(x)?

    <p>-4x<sup>2</sup> + 20x - 24</p> Signup and view all the answers

    Study Notes

    Wind Turbine Noise Level

    • A wind turbine's blades generate noise that can be measured at different distances.
    • Noise level (S(d)) is modeled by S(d) = abd, where S(d) is the noise level in decibels at a distance of d meters from the turbine.
    • At 0 meters, the noise level is 105 decibels.
    • At 100 meters, the noise level is 49 decibels.

    Equations for Noise Level

    • Using the given data, two equations can be constructed to find constants 'a' and 'b'.
    • 105 = ab0 (or simply 105 = a)
    • 49 = ab100

    Determining Constants 'a' and 'b'

    • a = 105 (from the equation 105 = a)
    • b = 0.992408 (solved by calculating b = (49/105)^(1/100))

    Average Rate of Change

    • The average rate of change of noise level between 0 and 100 meters is calculated using (S(100) - S(0)) / (100 - 0).
    • Average rate of change = -0.56 decibels per meter

    Interpretation of Average Rate of Change

    • On average, the noise level decreases by 0.56 decibels for each additional meter as the distance from the turbine increases from 0 to 100 meters.

    Estimating Noise Level at 120 Meters

    • Using the average rate of change, the noise level at 120 meters can be estimated.
    • Estimated noise level at 120 meters is approximately 37.8 decibels.

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    Description

    This quiz explores the noise levels generated by wind turbines at varying distances. It focuses on the equations used to model the noise level, the determination of constants 'a' and 'b', and the calculation of the average rate of change in noise level. Test your understanding of these concepts and their applications in real-world scenarios.

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