Half life Questions

Question

The half-life of substance A is 16 years, and substance B decays at a rate of 30 % each decade.

(a) Find a formula for a function f(t) that gives the amount of substance A, in milligrams, left after t years, given that the initial quantity was 100 milligrams. 

f(t)=

(a) Find a formula for a function g(t) that gives the amount of substance B, in milligrams, left after t years, given that the initial quantity was 100 milligrams. 

g(t)= 

Answer 1

f(t) = a₀(0.5)^t/16

g(t) = 100(0.70)^t/10

Answer 2

A(t) = Ao(1/2)^(t/16)

= f(t) = 100(1/2)^(t/16)

when half life = 16 years, initial amount =100

B(t)

= g(t) 100(.7)^(t/10)

when amount left after 10 years = 70%