Equation to find the amount left after t years

Question

Suppose that a sample initially contains N₀ grams of a radioactive substance. If this substance has a half-life of 32 years, then which of the following equations can be used to find the amount left after t years?

a. N(t)=N₀e^-0.0313t

b.  N(t)=N₀e^-3.4657t

 

c.  N(t)=N₀e^-0.0217t

d.  N(t)=N₀e-2.4023t

e. none of these

Answer 1

N(t) = amount remaining in t years = N₀e^-kt

 

Since N(32) = N₀/2, we have N₀/2 = N₀e^-32k

 

Divide by N_0:  1/2 = e^-32k

 

Take natural logs:  ln(1/2) = -32k

 

                                  k = ln(1/2)/(-32) ≈ 0.0217

 

N(t) = N₀e^-0.0217t  [Answer (c)]