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Zorluk: OrtaInterpreting Linear Relationships in Context

A city reservoir contains water that is released at a constant rate for river conservation. The volume of water, WW, in millions of gallons, remaining in the reservoir dd days after the release begins is modeled by the equation W=240−1.8dW = 240 - 1.8d. What is the best interpretation of the number 1.81.8 in this context?

  1. A
    The reservoir loses 1 million gallons of water every 1.8 days.
  2. B
    The initial volume of water in the reservoir before the release begins is 1.8 million gallons.
  3. The volume of water in the reservoir decreases by 1.8 million gallons each day.Cevap
  4. D
    The total duration of the controlled release is 1.8 days.

Cevap

The volume of water in the reservoir decreases by 1.8 million gallons each day.
The equation W=240−1.8dW = 240 - 1.8d is in slope-intercept form, where the slope is −1.8-1.8 and the yy-intercept is 240240. The slope represents the rate of change of the remaining volume of water with respect to time. A slope of −1.8-1.8 indicates that the volume of water, WW, decreases by 1.81.8 million gallons for every 11 day increase in the number of days, dd.

Adım Adım Çözüm

1
Identify the variables and constants in the given linear model.
In W=240−1.8dW = 240 - 1.8d, WW is the remaining volume in millions of gallons, dd is the time in days, 240 is the y-intercept (initial volume), and -1.8 is the slope (rate of change).
Understanding the components of a linear equation y=mx+by = mx + b helps isolate the meaning of each constant.
2
Interpret the meaning of the slope in the context of the variables and units.
The coefficient of dd is -1.8, which represents a rate of change of -1.8 million gallons per day.
The slope is the change in the dependent variable (WW, in millions of gallons) per unit change in the independent variable (dd, in days).
3
Relate the negative sign to the physical context.
A negative slope of -1.8 means that the volume decreases by 1.8 million gallons for each elapsed day.
In context, a constant release of water leads to a decrease in the remaining volume.

Anahtar Kavram

Interpreting slope in a linear relationship context
Tahmini Süre:1m 30s
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Interpreting Linear Relationships in Context

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