Answer :
Answer:
The answer is "[tex]1.4 \ \bold{ billion-years}[/tex]".
Explanation:
Using formula:
[tex]\to N_{Now} = N_{orige}e^{\lambda t} \\\\[/tex]
[tex]\to[/tex] 1 U atom produces 1 Pb atom after decay.
[tex]\to[/tex] U's original numbers are now the sum of U counts and Pb counts.
[tex]\to N_U=(N_U+N_{pb})e^{\lambda Ut}[/tex]
[tex]\to 1 = (1+3) \ exp[(\frac{-\ln(2)}{t_{(half)}} \times t ]\\\\\to t = [\frac{\ln(4)}{\ln(2)}] \times t_{(half)}[/tex]
[tex]= 14 \times 10^8 \ \ years\\\\=1.4 \ billion \ \ years[/tex]