# Science

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Radioactive substance decays so that after t years, the amount remaining, expressed as a percent of the original amount, is A(t)=100(1.6)^(-t).

a) Determine the function A’, which represent the rate of decay of the substance.

b) what is the half-life for this substance?

c) what is the rate of decay when half the substance has decayed?

• Science -

a) A' = dA/dt = -100*(1.6^-t)*ln1.6
= -47*1.6^-t
b) When A(t) = (1/2)A(0),
100*1.6^-t = 50
1.6^-t = 0.5
-t ln1.6 = ln0.5
t = 1.475

c) A' at t = 1.475 is half the rate at t = 0, or -23.5

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