need some help

[mattflint50]

I have two problems that i need help with.

the first is: 44g of a substance decays to 20g in 10 years. How long would it take for this substance to decay to 16g?

THe seconds is: Helium is pumped into a balloon at a rate of 225 cubic inches persecond. At what rate is it increasing when the balloon is 45 inches in diameter.


THanx

 

[Gene]

The decay formula is
W = W₀e^(-kt)
solve for k
20 = 44e^(-k*10)
20/44 = e^(-k*10)
ln(20/44) = -k*10 = -.78845
k=.078845
16 = 44e^(-.078845t)
Solve for t

Assuming a spherical balloon and you want the rate the radius is changing.
V = (4/3)*pi*r^3
Find dV/dr
From the chain rule
dr/dt = dV/dt / dV/dr
You know dV/dt = 225
Divide

 

[mattflint50]

i still dont understand the ballon problem, but for the decay problem i got about 12.9 years

 

[Gene]

Sounds close enough.
What is it you don't understand? Show your work.
---------------------
Gene

 

[mattflint50]

ok; I started out by finding using dv/dt=3*(4/3)pi r^2 dr/dt; the threes cancel so it becomes dv/dt=pi r^2 dr/dt; I already knew that dv/dt equaled 225 so i used 225=4 pi (22.5)^2 dr/dt; and it ends being .0354 inches per second.


Im not sure if im on the right track or not.

 

[Gene]

I started out by finding dv/dr=3*(4/3)pi r^2

dr/dt = (dv/dt)/(dv/dr) =
225/(4*pi*r^2) =
225/(4*pi*(22.5)^2) =
.0354
We're on parallel tracks and you understand just fine. Just two slightly different approaches to the same destination.
---------------------
Gene

 

[mattflint50]

Ok; thank you for your time and help

 

[~Midnight.Kitten~]

:shock: