Question

The fraction of a cohort of AIDS patients that survives a time t after AIDS diagnosis is given by S(t)=exp(-kt). The time it takes for s(t) to reach the value of 0.5 is defined as the survival half-life and denoted by T1/2.

PART A)

show that s(t) can be written in the form s(t)=2^(-1/(T1/2))

PART B)

show that T1/2= T aver ln(2), where T aver is the average survival time defined in problem (1). THus it is always ture that T1/2

Answer 1

I'll just use T to mean T1/2, for readability
2^(-1/T) = (e^ln2)^(-1/T) = e^(-ln2/T)
So, s(t) = e^(-kt) where k = ln2/T