The function Q(t)=Qe^-kt may be used to model radioactive decay. Q represents the quantity remaining after t years; k is the decay constant, 0.00011. How long, in years, will it take for a quantity of plutonium-240 to decay to 25% of it's original amount?

Question

anonymous · Answer

$$Q(t)=Q _{o}e ^{-kt}$$

ankit042 · Answer

q(t)= 0.25Q 
k =0.00011
Now you can solve for t

zzr0ck3r · Answer

Q_0 is the starting amount, (1/4)Q_0 is the ending amount
$$\frac{1}{4}Q_0=Q_0e^{-0.00011t} \rightarrow \frac{1}{4}=e^{-0.00011t}$$

solve for t

anonymous · Answer

I'm not sure if I did it right. Would it be approximately 12,600 years then?

zzr0ck3r · Answer

ln of both sides
ln(1/4) = -0.00011t
divide by -.00011
t = -ln(1/4)/0.00011

zzr0ck3r · Answer

yes
-ln(1/4)/0.00011 = 12602.7

anonymous · Answer

Okay, thank you!

zzr0ck3r · Answer

im not sure what @ankit042 was doing, maybe there is another way....