My question is
2. our family has a small pool for relaxing in the summer that holds 1500 gallons of water.
i decided to fill the pool for the summer. when i had 5 gallons of water in the pool, i
decided that i didn’t want to stand outside and watch the pool fill, so i wanted to figure
out how long it would take so that i could leave, but come back to turn off the water at
the right time. i checked the flow on the hose and found that it was filling the pool at a
rate of 2 gallons every 5 minutes. how many gallons of water will be in the pool after
50 minutes? how many minutes will it take to fill the pool? justify your answer with a mathematical model of the problem situation.
is the answer 2(n-1) + 5?

So 2 gallons every 5 minutes
2/5= .4
so .4 a minute
and you already have 5 gallons in so those need to be added
m=minutes
y=0.4m + 5 will be what you want to find out if you are looking to find out how much will be there in a certain time
for 50 minutes you will have
y=0.4(50) +5 
20+5
25 gallons
HOWEVER, the equation has to be changed if you want to tell how long you have to wait for it to fill.
m=2.5(g-5)
m=minutes
g= gallons
you subtract 5 because they are already there
you multiply by 2.5 because it fills at a rate of 1 gallon every 2.5 minutes.
m=2.5(1500-5)
for the sake of it being easier i will do the -5 separately
2.5(1500 = 3750
2.5(-5= -12.5
3750-12.5
3737.5 minutes to fill the pool.
3720/60 = 62
17.5/60 = .292
62.292 hours to fill the pool.
p.s. you have a really slow hose.
Its good you didn't wait for it to fill, you would have died from lack of water before then if you just sat and waited.