I need help with this calculus problem PLEASE!?

Question

The half-life of Carbon-14 is about 5700 years. If there is only 37 percent left of the C-14 originally present in an object, how old is the object?

Answer 1

if half life is 5700 years, it means that the full life for it to deplete is 5700x2=114,000 years

so ....0.37*114,000=4218 years left.
This means that the object is at least 109,782 years old(114,000-4218)

Answer 2

Hi,
We can find the time from this equation:
N = Noe^(-λt)…..(Eq1) (No is N sub o, the original amount.)
But first we need the disintegration constant λ. We can find that from the relationship:
λ= 0.693/T…(Eq2)(Where T is the half-life.)
=0.693/5700
=1.2157E-4
Substitute in Eq 1.
N= Noe^(-1.2157E-4t)
(0.37No)/No = e^(-1.2157E-4t)
.37 = e^(-1.2157E-4t)
ln 0.37 = -1.2157E-4t
t = ln( 0.37)/(-1.2157E-4
t=8139.135 years rounded to three decimal places.

FE