Question

on hot days, bruce fills a plastic swimming pool in the backyard for his dog, bella. he fills the pool using a garden hose with a flow rate of 12 gallons per minute. bellas pool can hold 60 gallons of water and takes 5 minutes to fill up to the maximum fill line. the function v(m) represents the volume of water in the pool, in gallons, after m minutes of filling it with the hose. what is the range of v(m)? all multiples of 5 from 0 to 60 all real numbers from 0 to 60 all whole numbers less than or equal to 60 all multiples of 12 from 0 to 60

Explanation:

Step1: Analyze the function

The volume function \( V(m) \) is related to the flow rate. The flow rate is 12 gallons per minute, so \( V(m)=12m \), where \( m \) is the time in minutes. The pool fills in 5 minutes (since \( 12\times5 = 60 \) gallons) and starts at 0 gallons.

Step2: Determine the domain of \( m \)

The time \( m \) starts at 0 (when filling begins) and goes up to 5 minutes (when the pool is full). So \( 0\leq m\leq5 \).

Step3: Find the range of \( V(m) \)

Substitute the domain values into \( V(m)=12m \). When \( m = 0 \), \( V(0)=0 \). When \( m = 5 \), \( V(5)=60 \). For values of \( m \) between 0 and 5, \( V(m) \) will take all real number values between 0 and 60 because the flow is continuous (water is added continuously, not in discrete amounts). So the range is all real numbers from 0 to 60.

Answer:

all real numbers from 0 to 60