Plutonium-240 decays according to the function Q(t)=Q(subscripto)e^(-kt) where Q represents the quantity remaining after t years and k is the decay constant, 0.00011... How long will it take 27 grams of plutonium-240 to decay to 9 grams?

Question

anonymous · Answer

A. 18,900 years
B. 2,100 years
C. 1.44 years
D. 9,990 years

campbell_st · Answer

you have$$Q(t) 9====>Q _{0}= 27 =====>k = 0.00011$$

then 

$$9 = 27 e^-0.00011t$$

or 

$$\frac{1}{3} = e^{-0.00011t}$$

take the base e log of both sides

$$\ln(\frac{1}{3}) = -0.00011t$$

$$t = \frac{\ln(\frac{1}{3})}{-0.00011}$$

all you need to do is evaluate t