Science
posted by jessica on .
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 halflife for this substance?
c) what is the rate of decay when half the substance has decayed?

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