Thursday

March 5, 2015

March 5, 2015

Posted by **deel** on Wednesday, August 8, 2012 at 9:35pm.

- math -
**MathMate**, Wednesday, August 8, 2012 at 10:23pmI assume you are familiar with integration or differential equations.

y(t)=amount of air (in c.f.) in room at time t.

Then

dy/dt

=y'(t)

=rate of increase of fresh air per unit time (min)

=fresh air in - fresh air out per minute

=600 - 600(y/20000)

=600*(20000-y)/20000

Separate variables and integrate:

∫dy/(20000-y) = (600/20000)∫ dt

-log(20000-y) = 600t/20000 + C'

log(20000-y) = -600t/20000 + C

Raise to power of e:

20000-y = e^(-600t/20000+C)

y=20000(1-e^(-600t/20000+C)

At t=0, y=0

=>

0=(1-e^(0+C))

=> C=0

Therefore:

y=20000(1-e^(-600t/20000))

at y=0.9*20000=18000,

=>

e^(-600t/20000)=0.1

t=-(20000/600)*log(0.1)

=77 minutes (approx.)

- math -
**deel**, Thursday, August 9, 2012 at 11:10amthanks for your help

- math :) -
**MathMate**, Thursday, August 9, 2012 at 11:40amYou're welcome!

**Answer this Question**

**Related Questions**

physics - a room that measures 10.o ft wide, 32.0 ft long, and 8.00 ft high ...

Precal - The equation is y=80.4- 11 ln x, 100<x<1500 Which approximates ...

physics - Consider a room air conditioner using a Carnot cycle at maximum ...

Physics - Air isn't a perfect electric insulator, but it has a very high ...

Math/ Science - If you squeezed all the air in a large living room into a small...

Physics - A room measures 4.0 m by 3.9 m by 4.5 m. The heating and air-...

chemistry - The density of air is 1.25 gram per liter determine the volume ...

AP Physics - A young male adult takes in about 4.0 10-4 m3 of fresh air during a...

Math/ Science - If you squeezed all the air in a large living room into a small...

AP Physics PLEASE HELP DUE TOMORROW - A young male adult takes in about 4.0 10-4...