Answer to Question #3663 in Algebra for tami

Question

I am trying to figure out how to do this question. The half-life of a substance is 120 days. The initial quantity is 72g.
A) Write the specific equation in the form A=A[sub]o[/sub] e[sup]kt[/sup].
B) How much will be left after 85 days?
C) How long until only 8 g is left?

Answer 1

a. 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
240ln(3)/ln(2) = 379 days.