ok its about math

Question

The mass of a radioactive element at time x is given by the equation below, where c is the original mass and h is the half-life of the element. How old is a mummy that has lost 57% of its carbon-14 (its half-life is 5730 years)? (Round your answer to the nearest year.)

Answer 1

m=2^-x/hc, where m is the mass.

We know that h=5730 years when m=½c (definition of half-life), so let's see if the formula works when x=5730 years:

½c=2^-1c, ½=1/2✔️

If the mummy has lost 57% of its C₁₄ then its mass m=0.43c.

From the formula: 0.43c=2^-x/5730c.

2^-x/5730=0.43,

(-x/5730)log(2)=log(0.43),

x=-5730log(0.43)/log(2)=6976.8 years, rounded to the nearest year is 6,977 years, so the mummy is about 6,977 years old.