A city reservoir contains water that is released at a constant rate for river conservation… — SAT

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

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

Answer

The volume of water in the reservoir decreases by 1.8 million gallons each day.

The equation

W = 240 - 1.8d

is in slope-intercept form, where the slope is

-1.8

and the

y

-intercept is

240

. The slope represents the rate of change of the remaining volume of water with respect to time. A slope of

-1.8

indicates that the volume of water,

W

, decreases by

1.8

million gallons for every

1

day increase in the number of days,

d

Step-by-Step Solution

Identify the variables and constants in the given linear model.

W = 240 - 1.8d

W

is the remaining volume in millions of gallons,

d

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 + b

helps isolate the meaning of each constant.

Interpret the meaning of the slope in the context of the variables and units.

The coefficient of

d

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 (

W

, in millions of gallons) per unit change in the independent variable (

d

, in days).

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.

Key Concept

Interpreting slope in a linear relationship context

Estimated Time:1m 30s

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