How many years has passed if only 3.125% of the original amount of U-238 remains?
Given
R=0.03125R0R=0.03125R_0R=0.03125R0
T1/2=4.5×109yearsT_{1/2}=4.5×10^9 yearsT1/2=4.5×109years
The amount of radioactivity present after time t is
R=R0e−tln2t1/2R=R_0 e^{-\frac{tln2}{t_{1/2}}}R=R0e−t1/2tln2
0.03125R0=R0e−tln24.5×109years0.03125R_0=R_0 e^{-\frac{tln2}{4.5×10^9 years}}0.03125R0=R0e−4.5×109yearstln2
t=2.25×1010yearst=2.25 \times 10^{10} yearst=2.25×1010years
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