To interpret the function \( y = 55 - 2.8x \), we can analyze its components:
- The variable \( y \) represents the amount of water in the bathtub (in gallons).
- \( x \) represents the time in minutes.
- The constant \( 55 \) indicates the initial amount of water in the bathtub before it starts draining.
- The term \( -2.8x \) indicates that the water is draining at a rate of 2.8 gallons per minute.
Now, let's analyze the provided statements:
A. The bath is draining at a rate of 55 gallons per minute.
- This statement is incorrect because the rate of drainage is -2.8 gallons per minute (not 55).
B. The amount of water in the bath increases by 2.8 gallons each minute.
- This statement is incorrect because the amount of water decreases by 2.8 gallons each minute as time progresses.
C. Before any water drained, the bath contained 2.8 gallons of water.
- This statement is incorrect because it does not reflect the initial amount. The function at \( x = 0 \) yields \( y = 55 \), not 2.8.
D. Before any water drained, the bath contained 55 gallons of water.
- This statement is correct. When \( x = 0 \), \( y = 55 - 2.8(0) = 55 \), indicating that there were 55 gallons in the bathtub initially.
Thus, the correct interpretation is:
D. Before any water drained, the bath contained 55 gallons of water.