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Difficulty: MediumInterpreting Linear Relationships in Context

An agricultural drone is used to spray liquid fertilizer on a field. The volume of fertilizer remaining in the drone's tank, FF, in liters, can be modeled by the equation F=120−4.8tF = 120 - 4.8t, where tt is the number of minutes after the drone begins spraying. What is the best interpretation of the number 4.84.8 in this context?

  1. A
    The volume of fertilizer, in liters, in the drone's tank before the spraying operation begins.
  2. The volume of fertilizer, in liters, that is sprayed from the drone's tank each minute.Answer
  3. C
    The number of minutes it takes for the drone to spray one liter of fertilizer.
  4. D
    The number of minutes the drone can spray fertilizer before the tank is completely empty.

Answer

The volume of fertilizer, in liters, that is sprayed from the drone's tank each minute.
In the linear equation F=120−4.8tF = 120 - 4.8t, the variable FF represents the remaining fertilizer in liters, and tt represents the elapsed time in minutes. The value 4.8 is the coefficient of tt, which represents the rate of change of the fertilizer in the tank. The negative sign in front of 4.8 indicates a decrease over time, meaning that the drone sprays 4.8 liters of fertilizer from the tank each minute.

Step-by-Step Solution

1
Identify the role of the constant 4.8 in the given linear equation F=120−4.8tF = 120 - 4.8t.
The coefficient of the independent variable tt is −4.8-4.8, which represents the slope of the linear relationship.
In the slope-intercept form of a linear equation, the coefficient of the variable represents the rate of change (slope).
2
Interpret the meaning of the slope in the context of the problem.
Since FF is measured in liters and tt is measured in minutes, the slope represents a change in liters per minute. The negative sign indicates that the volume of fertilizer is decreasing.
The rate of change is the change in the dependent variable (liters of fertilizer) divided by the change in the independent variable (minutes).
3
Select the option that correctly describes this rate of change.
The rate of decrease is 4.8 liters per minute, which means 4.8 liters of fertilizer are sprayed from the tank each minute.
This matches the definition of the rate at which fertilizer is leaving the tank.

Key Concept

Interpreting the slope of a linear equation in a real-world context.
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Topics

Interpreting Linear Relationships in Context

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