Question

a radioactive sample has a decay rate R of 518 decay/min at time t=7 min and 156 decay/ min at time t=17 min. calculate the decay constant and the initial decay rate?

Answer 1

a = Ai e^-kt
da/dt = -kAi e^-kt

518 = -k e^-7k

156 = -k e^-17k

518/156 = e^-7k / e^-17k = e^10k

ln 3.32 = 10 k

1.2 = 10 k
k = .12

I guess you can take it from there

Answer 2

assuming an exponential function with initial value f(t) = a,

a*e^-kt, we have

a*e^-7k = 518
a*e^-17k = 156
so, dividing, e^10k = 156/518
k = -0.12

f(t) = ae^-.12t
a*e^-.84 = 518
a = 1200

f(t) = 1200 e^-0.12t