Answer to Question #3676 in Algebra for tami

Question

The half-life of a substance is 120 days. The initial quantity is 72g.
a. Write the specific equation in the form A=Aoekt

b. How much will be left after 85 days?

c. How long until only 8 g is left?

Answer 1

A=A₀e^-kt.
1/2 A₀= A₀e^-kτ
Where τ is a half-life period. So we get
K=ln(2)/ τ
We have
A=A₀e^{- ln(2)t/ τ} = 72e^{- ln(2)t/120}.
b.
A= 72e^{- ln(2)85/120} = 44.17 g.
c.
8= 72e^{- ln(2)t/120} -> 1/9=72e^{- ln(2)t/120} -> -2ln(3)= - ln(2)t/120
240 ln(3)/ln(2) = 379 days.