Integral Applications: Rate of Change

[olicoh]

Homework Statement

The volume of an air mattress is 15 cubic feet. Air escapes at a rate of r(t)=0.25e^(−0.05t), where r is in cubic feet per second. Assuming the mattress is still completely inflated when the valve is opened, how much air is released in the first 30 seconds?

Homework Equations

Here is what I have so far:
V(15) = V(0) + integral[0,15] (0.25e^(-0.05t))
= [-(1/2) (e^(-1/2t))]¹⁵₀ <-- Sorry, I don't know any other way to write the upper/lower bound.

The Attempt at a Solution

= -2.765E-4 - -0.5

Ugh... My problem with this question is I don't even know what to do for the first step. I just used a formula that was in my textbook and inserted numbers. What is the V(15) and V(0) for anyways? What formula should I be using for this problem?EDIT: I redid the problem and got 0.4997 cubic feet of air is released per second, roughly. Is that right?

 

[tiny-tim]

welcome to pf!

hi olicoh! welcome to pf!

(have an integral: ∫ and try using the X² icon just above the Reply box )

… What is the V(15) and V(0) for anyways?

i've no idea

V(t) should be the volume at time t …

so V(0) = 15, and dV/dt = r

start again ​

 

[olicoh]

hi olicoh! welcome to pf!

(have an integral: ∫ and try using the X² icon just above the Reply box )


i've no idea

V(t) should be the volume at time t …

so V(0) = 15, and dV/dt = r

start again ​

Thank you! Oh ok... I don't know. My textbook seriously does not explain any of this stuff to me. they give me equations but they don't provide me an explanation. I'm basically always confused.

 

[tiny-tim]

… they give me equations but they don't provide me an explanation.

that's to encourage you to work out the equations for yourself …

have a go ​