Differentiation

K

kimbero5

New member
Joined
Sep 11, 2005
Messages
20
Supposed W(t) denotes the amount of a radioactive material left after time t. Assume that W(0)=15 and that
dW/dt=-2W(t)
a. how much material is left at time t=2?
b. What is the half life of this material?

how do i get the formula so that i can plut 15 in for W(0) and then once i have that formula i can plug in 7.5 for the half life right?
 
You are given dW/dt = -2W(t). Then dW/W(t) = -2dt. Integrate both sides to find a formula for W(t).

You are given that W(0) = 15. So plug "0" in for "t" in your formula for W(t), and solve for the value of the constant of integration.

Now you have the formula for W(t).

a) Plug in "2" for "t". Simplify to get the answer.

b) Plug in "7.5" for "W", and solve for the value of t.

If these instructions don't make sense within the context of what you've covered so far, then please reply showing what you have tried, so we can see what methodology you're supposed to be using.

Thank you.

Eliz.
 
so then dW/W(t)=-2dt which = 0 when you plug 0 in for t

then dW/15=0 so either W or d = 0 but which one?
 
I'm sorry, but I don't understand your post. Where is "dW/15 = 0" coming from, when you were only given that W(0) = 15?

Please reply with clarification. Thank you.

Eliz.
 
W(0)=15 and i plugged W(0) in to get the dW/15 and i plugged in 0 for t on the other side to make it all equal to 0
 
Then where is "dW/W(0) = t" coming from? How did you derive this?

Eliz.
 
You must log in or register to reply here.
Top