Answer to Question #3663 in Algebra for tami

Question #3663
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?
Expert's answer
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.

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