Find an exponential rule that would model the amount of Tc-99m left in the person at any time t in days.

Question

Tc-99m is used to detect tumors in the body. The half life of Tc-99m is only 6 hours. Suppose an initial dosage of 20 mCi was administered. Find the rule.

Answer 1

The rule is

 

A(t) = A₀(1/2)^t/T

 

A(t) = amount remaining at time t

 

A₀ = initial amount (at time t = 0)

 

t = time in hours

 

T = half-life = 6 hours

 

A(t) = A₀(1/2)^t/6

 

If you want to work with t in days, then replace the half-life of 6 hours with 1/4 of a day (6 hours = 1/4 of a day).  

 

A(t) = A₀(1/2)^t/(1/4) = A₀(1/2)^4t with t in days

 

Be careful with the units.