Inment A 600-gallon tank is initially full of water and is being drained at a rate of 30 gallons per minute. Complete parts (a) through (d) below. Question \( 46,2.4 .19 \) The \( W \)-intercept is \( (0,600 \) of 8 (Type an ordered pair.) Interpret the \( W \)-intercept. Choose the correct answer below. \( 80.25 \%, 47.35 \) of 59 points A. The \( W \)-intercept is the time it takes to empty the tank. B. The \( \mathbf{W} \)-intercept is the constant rate of change of water in the tank. C. The \( W \)-intercept is the initial amount of water in the tank. (d) Find the domain of \( W \). Choose the correct domain of \( W \) below. A. \( D=\{t \mid \leq t \leq \square\} \) B. All real numbers.
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The Deep Dive
The \( W \)-intercept at \( (0,600) \) signifies that when time \( t = 0 \), the tank is full with 600 gallons of water. This initial value serves as a critical point in understanding how the water level changes over time as the tank drains. It reflects the maximum capacity of the tank, which is vital for setting up an equation that models the draining process. When considering the domain of \( W \), you want to think about how time affects the volume of water in the tank. Since the tank starts full and drains until it reaches empty, the appropriate domain is \( D = \{t \mid 0 \leq t \leq 20\} \), as it takes 20 minutes to completely drain the tank at 30 gallons per minute.
