Sure! Let's analyze the equation given:
[tex]\[ w = 34 - 0.5d \][/tex]
This equation models the water level [tex]\( w \)[/tex] in feet of a river after [tex]\( d \)[/tex] days.
To understand the coefficient of [tex]\( d \)[/tex], let's break down the equation:
1. Constant Term [tex]\( 34 \)[/tex]: This is the initial water level in feet, before any days have passed. It represents the starting water level of the river.
2. Coefficient of [tex]\( d \)[/tex]: This is the term [tex]\(-0.5\)[/tex] that is multiplied by [tex]\( d \)[/tex], where [tex]\( d \)[/tex] represents the number of days.
The coefficient of [tex]\( d \)[/tex], which is [tex]\(-0.5\)[/tex], tells us how the water level changes with respect to time (days). Specifically:
- Rate of Change: The coefficient [tex]\(-0.5\)[/tex] indicates that for each day ([tex]\( d \)[/tex]), the water level decreases by 0.5 feet.
- Negative Sign: The negative sign shows that the water level is decreasing over time.
- Interpretation: For every additional day that passes, the water level [tex]\( w \)[/tex] decreases by 0.5 feet. This means there is a consistent drop in the water level by half a foot every day.
To summarize, the coefficient of [tex]\( d \)[/tex] in the equation [tex]\( w = 34 - 0.5d \)[/tex] signifies the rate at which the water level of the river decreases over time. In this case, it decreases by 0.5 feet per day.
