The halflife of nitrogen13 is approximately 997 minutes Dete

The half-life of nitrogen-13 is approximately 9.97 minutes.

Determine a so that A(t)=A₀a^t describes the amount of nitrogen-13 left after t minutes, where A₀ is the amount at time t=0. found to six decimal places.

a= ?

Solution

A(t) = Aoa^t

A(t) = Ao/2 at t= 9.97 min.

Ao/2 = Aoa^9.97

0.5 = a^9.97

taking natural log on both sides:

ln(0.5) = 9.97ln(a)

ln(a) =-0.0695

a = e^(-0.0695) = 0.932860