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. (a) Write a formula for a linear function W that gives the number of gallons of water in the tank after t minutes. \( W(t)=\square \) (Tvoe an expression using \( t \) as the variable. Do not factor.)

To find the formula for the number of gallons of water in the tank after \( t \) minutes, we start with the initial amount of water in the tank, which is 600 gallons. Since the tank is being drained at a rate of 30 gallons per minute, we deduct the drained amount from the initial volume. Thus, the function can be expressed as: \( W(t) = 600 - 30t \). Now, let's move on to the real-world applications of such functions. In real life, understanding how linear functions work helps us manage resources effectively. For example, if you’re running a fish tank or a reservoir, knowing how quickly water levels change can help in scheduling water replacement or alerting to potential shortages. You can prevent overflows or critically low water levels by applying this knowledge practically. Additionally, a common mistake in setting up similar problems is neglecting to consider units. When using rates (like gallons per minute), always ensure consistency in measurement. If you were to use a different time unit without converting, for example, calculating for seconds instead of minutes, you would miscalculate the total water drained. Always keep track of those pesky units!