An agricultural drone is used to spray fertilizer on a crop field. The volume of fertilize… — SAT

An agricultural drone is used to spray fertilizer on a crop field. The volume of fertilizer remaining in the drone's tank, $F$ , in liters, after the drone has been spraying for $t$ minutes is modeled by the equation $F = 240 - 3.2t$ , where $0 \leq t \leq 75$ . What is the best interpretation of the number $3.2$ in this context?

A
The initial volume of fertilizer, in liters, in the tank before spraying begins.
B
The number of minutes required for the drone to spray $1$ liter of fertilizer.
The volume of fertilizer, in liters, sprayed from the tank each minute.Answer
D
The total number of minutes the drone can spray before the tank is completely empty.

Answer

The volume of fertilizer, in liters, sprayed from the tank each minute.

In the linear relationship

F = 240 - 3.2t

, the variable

t

represents time in minutes, and

F

represents the remaining volume in liters. The coefficient of

t

, which is

-3.2

, represents the rate of change of the volume of fertilizer in the tank. A slope of

-3.2

means that the volume decreases by

3.2

liters for every additional minute of spraying. Therefore, the number

3.2

represents the volume of fertilizer, in liters, that is sprayed from the tank each minute.

Step-by-Step Solution

Identify the structure of the linear equation.

The equation is of the form

y = mx + b

, or in this case,

F = -3.2t + 240

, where the slope is

-3.2

and the

F

-intercept (initial value) is

240

Analyzing the components of a linear function helps determine what each constant represents in context.

Determine the meaning of the slope in context.

The slope is the coefficient of the independent variable

t

(time in minutes). The value

-3.2

indicates that for each increase of

1

minute in spraying time, the remaining volume of fertilizer,

F

, decreases by

3.2

liters.

Slope represents the rate of change of the dependent variable relative to the independent variable.

Interpret the absolute value of the slope.

The value

3.2

represents the magnitude of this rate, which is the amount of fertilizer sprayed out of the tank per minute (

3.2

liters per minute).

Matching the mathematical rate of change to the corresponding verbal description provides the correct interpretation.

Key Concept

Slope in a linear model represents the constant rate of change of the dependent variable per unit increase of the independent variable.

Estimated Time:1m 15s

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