You are filling a 19,400 gallon pool, w. The pool fills at a rate of 8 gallons per minute, m. The amount of water in the pool at any given minutes can be found using the equation. What is the domain and range.
assuming you start at time m=0, with w(0) = 0
That is, with an empty pool,
w(m) = 8m
19400gal / (8gal/min) = 2425 min
So, the domain is [0,2425]
the range is [0,19400]
To determine the domain and range of the given equation, we need to understand the meaning of the variables involved.
In this equation, "w" represents the amount of water in the pool at any given minute, and "m" represents the number of minutes that have passed. We know that the pool fills at a rate of 8 gallons per minute.
1. Domain:
The domain is the set of possible values for the independent variable, which in this case is the number of minutes (m). Since time cannot be negative and the pool is being filled continuously, the domain would start from 0 minutes and continue indefinitely. Therefore, the domain is m ≥ 0, which means any non-negative real number.
2. Range:
The range is the set of possible values for the dependent variable, which is the amount of water in the pool (w). The amount of water in the pool increases by 8 gallons every minute. Therefore, the minimum amount of water in the pool is 0 gallons (when no time has passed), and the maximum amount of water is the capacity of the pool, which is given as 19,400 gallons. Hence, the range is 0 ≤ w ≤ 19,400, which means any non-negative number less than or equal to 19,400.
In summary, the domain is m ≥ 0 (all non-negative real numbers) and the range is 0 ≤ w ≤ 19,400 (all non-negative numbers less than or equal to 19,400).