The Amount At, micrograms of a certain radioactiv substance remaining after t years decreases according to the formula At=Aoe^-0.002t , where Ao is the amount present initially

a) If 600 micrograms are left after 1000years, how many micrograms were present initially?

b) The half-life of a substance is the time taken for the amount to decrease to half of its initial amount. What is the half-life of this substance?


:confused:

The Amount At, micrograms of a certain radioactiv substance remaining after t years decreases according to the formula At=Aoe^-0.002t , where Ao is the amount present initially


a) If 600 micrograms are left after 1000years, how many micrograms were present initially?

Set the equation equal to 600 and t=1000, then solve for A_{0}


b) The half-life of a substance is the time taken for the amount to decrease to half of its initial amount. What is the half-life of this substance?

You are given k=-.002. Half-life is given by the formula T=\frac{-1}{k}ln(2)

Just plug in k.

HaHa.. I remember doing these questions in earlier classes.

Nyways,
a) 600 = Ao*e^(-0.002*1000) Find A0
b) In 2nd part, you are given,A=A0/2, therefore A/a0 =1/2
Use in eqn. given and find t

Good luck dear. Best of luck with your exams

@galactus
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