Question

Due to winter, the Maxwells want to drain their swimming pool. The function below represents the amount of water in the pool after I minutes of draining.

V(t) = 15,000 - 50t

What is the domain of V(t)?
A. all real numbers
B. all positive integers less than or equal to 3,000
C. all real numbers between and including 0 and 3,000
D. all real numbers less than 3,000

Answer 1

The domain of V(t) = 15,000 - 50t is all real numbers between and including 0 and 300, because these values represent the time in minutes during which the pool is being drained and contain no negative values for water volume. The correct answer is option A. all real numbers.

Step-by-step explanation:

Understanding the Domain of V(t)

The domain of V(t) = 15,000 - 50t represents the set of all permissible input values (time in minutes, in this case) for which the function V(t) gives a valid amount of water remaining in the pool. Since the pool cannot have negative water, the function is only valid when V(t) ≥ 0.

This results in a domain for t such that 0 ≤ t ≤ 300, because after 300 minutes, the water amount would reach zero, following the draining rate of 50 liters per minute. Thus, the correct domain for V(t) is all real numbers between and including 0 and 300. This makes the correct answer Option C. It's important to note that t must be non-negative since you can't drain a pool for a negative amount of time.

We find the domain by setting V(t) to be greater than or equal to zero:
0 ≤ 15,000 - 50t
Solving this inequality for t gives:
0 ≤ t ≤ 300