Now try a real-world example with more than 100 atoms. start with 5.4 × 1012 radioactive nuclei of lincolnium. approximately how many nuclei would still be radioactive after four half-life cycles?

Answer is: number of radioactive nuclei of Lincolnium is 3.375×10¹¹.

Half-life is the time required for a quantity (in this example number of radioactive nuclei of lincolnium) to reduce to half its initial value.
Initial number of nuclei: 5.4×10¹².
After first half-life: 50% · 5.4×10¹² ÷ 100% = 2.7×10¹².
After second half-life: 0.5 · 2.7×10¹² = 1.35×10¹².
After third half-life: 0.5 · 1.35×10¹² = 6.75×10¹¹.
After fourth half-life: 0.5 · 6.75×10¹¹ = 3.375×10¹¹.