Only 35% of the carbon-14 in a wooden bowl remains. How old is the bowl? Carbon-14 has a half-life of 5,700 years

Question

URGENT

Answer 1

A = a₀(0.5)^t/5700

0.35a₀ = a₀(0.5)^t/5700

0.35 = (0.5)^t/5700

ln 0.35 = ln [0.5^t/5700]

ln 0.35 = (t/5700) ln 0.5

-1.04982212 ≈ (t/5700)(-0.693147181)

-5983.98608 ≈ -0.693147181t

8633.06704 ≈ t

 

35% remains after approximately 8633 years.