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after a rain - storm, the water in a trough begins to evaporate. the amount in gallons remaining after t days is given by v = 46 - 1.6t.
identify the initial value and the rate of change, and explain their meanings in practical terms using units.
the initial value is
it represents
the rate of change is
it represents
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Explanation:

Step1: Identify the initial - value

The formula for the amount of water $V = 46-1.6t$. When $t = 0$ (at the start, right after the rain - storm), $V=46 - 1.6\times0=46$. So the initial amount of water is 46 gallons.

Step2: Identify the rate of change

The formula $V = 46-1.6t$ is in the form $y = mx + b$, where $m$ is the slope (rate of change). Here, $m=-1.6$. The negative sign indicates that the amount of water is decreasing. The value 1.6 means that 1.6 gallons of water evaporate each day.

Answer:

The initial value is 46. It represents the initial amount of water in the trough in gallons.
The rate of change is -1.6. It represents the amount of water (in gallons) that evaporates per day.