Question

Help! A swimming pool can hold a max of 360 gallons of water. The full pool develops a leak and is losing water at a constant rate. After 3 hours, the pool has 354 gallons of water in it. Write a function for g(t), the total number of gallons of water in the pool that is written in terms of t, the amount of time measured in hours that the leak developed.

Answer 1

@timo86m hi tim i see youre online, any chance you could help me with this problem?

Answer 2

oh that was easier than i thought. and if the leak is fixed after 20 hours and the owner immediately begins to refill the pool at a rate of 4 gallons of water per hour, write a piecewise functions for p(t), the total # of gallons of water that is in the pool for any time t, measured in hours.

Answer 3

360-g(20) + 4 t when t>20

Answer 4

wait is 360-g(20) + 4 t when t>20 the answer or is it the first one you posted?

Answer 5

the second one is right :)

Answer 6

oh ok and sorry one more question, if we solve for g(20), what does that represent?

Answer 7

use the formula i gave you
g(t)=118*t
g(20)=118*20

Answer 8

yes and i get 2360, but what does that represent?

Answer 9

oh wait i did it wrong read it wrong lol

Answer 10

haha darn

Answer 11

it is g(t)=3/2 *t

Answer 12

that is the function and g(t)=118t is wrong?

Answer 13

yes i thought it meant after 3 hours it lost 354 not it went fro m360 to 354 i adjusted for it now tho :)

Answer 14

oh ok so how did you get 3/2?

Answer 15

so now your piece wise function is
360-g(t) when t is 0 to 20
360-g(20)+4*t when t>20

Answer 16

ok and where did you get 3/2 from? and what does g(20), which is 30, represent?

Answer 17

3/2 comes from (360-354)/3=3/2

Answer 18

30 is the amount of water leak after 20 hours

Answer 19

ohh ok but isnt 360-354=6 and 6/3=2?

Answer 20

yes good catch lol i typed it in as 6/4 in my calculator

Answer 21

btw your piece wise funtion is still right :)

Answer 22

so now your piece wise function is
360-g(t) when t is 0 to 20
360-g(20)+4*t when t>20

Answer 23

haha ok cool does and lol i was just going to ask that!

Answer 24

because g(t) can later be modified and adjusted :)

Answer 25

alright i got it thank you very much! :)

Answer 26

do you think you could help me with some others if i post it?

Answer 27

i'll be way slow but i can try lol.

Answer 28

haha its ok! and thanks! ill post it in another question

Answer 29

ok i posted it