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Zorluk: ZorInterpreting Linear Relationships in Context

A commercial drone delivery service models the total power remaining in a drone's battery, P(w)P(w), as a percentage, after carrying a payload of weight ww kilograms for a fixed delivery distance of 10 kilometers. The relationship is modeled by the linear function P(w)=−8.5w+92P(w) = -8.5w + 92. Which of the following is the best interpretation of the value 92 in this context?

  1. A
    The decrease in the remaining battery power, as a percentage, for each increase of 1 kilogram in payload weight.
  2. B
    The remaining battery power, as a percentage, after the drone carries a payload of 1 kilogram for the delivery distance.
  3. The remaining battery power, as a percentage, after the drone carries a payload of 0 kilograms for the delivery distance.Cevap
  4. D
    The payload weight, in kilograms, for which the remaining battery power after the delivery is 0 percent.

Cevap

The remaining battery power, as a percentage, after the drone carries a payload of 0 kilograms for the delivery distance.
The linear equation is written in the slope-intercept form P(w)=mw+bP(w) = mw + b, where b=92b = 92 is the vertical intercept (y-intercept). This intercept represents the value of the dependent variable, P(w)P(w), when the independent variable, ww, is equal to 00. In this context, ww is the payload weight in kilograms and P(w)P(w) is the remaining battery power as a percentage. Thus, the value 9292 represents the remaining battery power, as a percentage, when the drone carries a payload of 00 kilograms.

Adım Adım Çözüm

1
Identify the structure of the linear function and the component being interpreted.
The linear equation is given in slope-intercept form, P(w)=mw+bP(w) = mw + b, where m=−8.5m = -8.5 is the slope and b=92b = 92 is the P(w)P(w)-intercept (y-intercept).
Understanding the components of a linear function allows us to relate them to their contextual definitions.
2
Evaluate the value of the function at the P(w)P(w)-intercept where the independent variable is zero.
Substitute w=0w = 0 into the equation: P(0)=−8.5(0)+92=92P(0) = -8.5(0) + 92 = 92.
The y-intercept represents the value of the dependent variable when the independent variable is equal to 0.
3
Interpret the meaning of w=0w = 0 and P(0)=92P(0) = 92 in the given context.
Since ww represents the payload weight in kilograms and P(w)P(w) represents the remaining battery power as a percentage, w=0w = 0 corresponds to a payload of 0 kilograms, and P(0)=92P(0) = 92 corresponds to a remaining battery power of 92%.
Applying the units and definitions of the variables completes the contextual interpretation of the constant.

Anahtar Kavram

Interpreting the y-intercept of a linear function in a real-world context
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Konular

Interpreting Linear Relationships in Context

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