# Answer on Algebra Question 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

B) How much will be left after 85 days?

C) How long until only 8 g is left?

A) Write the specific equation in the form A=A

_{o}e^{kt}.B) How much will be left after 85 days?

C) How long until only 8 g is left?

Expert's answer

a. A=A

1/2 A

Where τ is a half-life period. So we get

K=ln(2)/ τ

We have

A=A0e

b. A= 72e

c. 8= 72e

1/9=72e

-2ln(3)= - ln(2)t/120

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

_{0}e^{-kt}.1/2 A

_{0}= A_{0}e^{-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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