Question

Max values of a function

Answer 1

\[E(t) = \frac{ 13500 }{ t+1 }\]
\[L(t)=\frac{ 4500t+250 }{ t+1}\]

Answer 2

\[126000 \] gallons at t=0

Answer 3

E(t) and L(t) represent rates at which water enters/leaves the lake.

Answer 4

Please help!

Answer 5

can you take derivative ?

Answer 6

I didnt think i had to bc the functions represent rates.

Answer 7

to get max or min value, you need to equate the first derivative of the functions to 0

Answer 8

Right but the functions already represent the derivative bc they're rates. Maybe im mistaken. But thats what ive been taught.

Answer 9

ohh...can you post the entire question ?

Answer 10

Sure, gimme a sec to type please.

Answer 11

During a recent storm, water entered a lake through a stream and left through a spillway over a dam. The water entered at a rate given by the function \[E(t)=\frac{ 13500 }{ t+1 }\] and left the lake at a rate given by the function \[L(t)=\frac{ 4500t+250 }{ t+1 }\].. Both rates are in terms of gallons per hour and \[t\] is time in hours. At \[t=0\]the lake contained \[126000\] gallons of water.

Answer 12

I did parts a,b, and c.

Answer 13

Part d: At what time does the lake reach it maximum volume?
Part e: What is the maximum volume of the lake?

Answer 14

so, to get max. volume, e(t) should be maximum and l(t) should be minimum, right ??

Answer 15

max, water should enter lake and min water shouldd leave the lake, to get max volume, make sense ?
and yes, since they are rates, you'll just put t=0 in them.

Answer 16

Ohh, that simple?

Answer 17

So E(0) = 13500, L(0) =250

Answer 18

no, actually, sorry.
rates are to be equated to 0
so, e(t) =0 and l(t) = 0
actually, increase in volume will be proportional to
e(t) - l (t)
so, equate that to 0

Answer 19

do you have answers to verify ?

Answer 20

Thats what I did before. I did E(t)-L(t)=0, thus E(t)=L(t), when t= 2.944

Answer 21

isn't that correct ?

Answer 22

I wasnt sure.

Answer 23

well, i get the same. so you can be sure now.

Answer 24

Thanks. Brb

Answer 25

part e)
max volume = 126000+e(2.944)-l(2.944)
see whether this makes sense.

Answer 26

Ohh, hmm..ill try that.