a rock has a half life of 2.3 billion years, 40% element and 60% lead, how old is the rock

Question

A certain element has a half life given in cell B3, meaning that in that number of years, half of the element has turned to lead. You find a rock with the percent of the element and percent of lead given in cells B4 and B5. Find the age of the rock and enter it in Cell B6. Give your answer correct to two decimal places.

Answer 1

0.40a₀ = a₀(0.5)^t/2.3

0.40 = (0.5)^t/2.3

ln 0.4 = (t/2.3)(ln 0.5)

-0.916 ≈ (t/2.3)(ln 0.5)

-2.107 = t ln 0.5

-2.107 = -0.693 t

3.040 ≈ t