Question

Radium decays according to the function


formula in the comments*

where Q represents the quantity remaining after t years and k is the decay constant 0.00043. What is the half-life of radium?
Calculate how long it will take for 120g of radium to decay to 60g. Round your answer to the nearest year.

A. 55,813 years
B. 12 years
C. 806 years
D. 1612 years

Answer 1

\[Q(t)=Q _{0}e^-kt\]

Answer 2

@phi can you help please

Answer 3

@e.mccormick can you help me please??

Answer 4

@saifoo.khan can you help me

Answer 5

if use your equation, and set the amount to 1/2 of what we started with:
\[ Q(t)=Q _{0}e^{-kt} \\ \frac{Q_0}{2} = Q_0e^{-kt} \]
simplify by dividing both sides by Q0
we get (flipping sides so e is on the left ):
\[ e^{-kt} = 0.5 \]
take the natural log of both sides:
\[ \ln\left( e^{-kt} \right) = \ln(0.5) \\
-0.00043t = -0.69314718 \\
t = \frac{0.69314718}{0.00043} =1611.97
\]
rounded to the nearest year
t= 1612