Andrew measures the amount of a very unstable substance to be 100 moles. The half life of this substance is 3 days. Write an exponential function that models it

Question

Write an exponential function that models this situation where y is the amount of substanxe and x is time in days 

Answer 1

This is an exponential decay situation.  Let A(t) = amount present at time t.  Since after every 3 days the amount drops to 1/2 the starting amount, 

 

A(t) = A(0)(1/2)^t/3

 

t = number of days

A(0) = initial amount = 100 moles

 

A(t) = (100 moles) (1/2)^t/3, t in days