A scientist is studying a piece of cloth from an ancient burial site.?
Half-life of C14 given as 5730 years in various sources. Log_2(1/0.40) = 1.322. (5730 years)*(1.322) = 7575.06 yrs, round up to 7600 years.
Roger the Mole
I don't see any carbon decay graph, so using a half life of 5707.76 years for carbon-14: Let z be the age (in years) to be found: 0.40 = (1/2)^(z / 5707.76 years) log 0.40 = (z / 5707.76 years) x log (1/2) log 0.40 / log (1/2) = z / 5707.76 years z = 5707.76 years x log 0.40 / log (1/2) = 7545 = 7500 years
No. Cloth doesn't usually survive. It's usually metal or pottery.