Algebra homework help me!

Question

The radioactive element​ carbon-14 has a​ half-life of 5750 years. A scientist determined that the bones from a mastodon had lost

64.4​%

of their​ carbon-14. How old were the bones at the time they were​ discovered?

Answer 1

half life = -ln(2)/k where k is the coefficient inside the exponential

5750 = -ln(2)/k

k = -ln(2)/5750

so the decay function is y = C * exp( -ln(2)/5750 t) where C is the starting quantity , 64.4% of which remains at the time of discovery.

to 64.4% * C = C * exp( -ln(2)*t/5750 )

0.644 = exp( -ln(2)*t/5750)

ln(0.644) = -ln(2)*t/5750

ln(0.644)*5759 / -ln(2) = t

t = 0.366512920582*5750 =2107