Determine the half life of the substance that decays from Ao to A in time t

Question

Ao= 49 A=20 t=20 hours

the answer is 15.5 hours but how do I solve for h when its in the exponent?

Answer 1

20 = 49(.5)^20/h

 

Doris I assume you got this far based on the fact you did not know how to solve for h.

 

20/49 = (.5)^20/h

 

Take the natural log of both sides (any base works but ln is customary).

 

ln (20/49) = ln (.5)^20/h

 

ln (20/49) = 20/h ln (.5)

 

Isolate h to get something like this:

 

h = 20 ln(.5)/ ln (20/49)