A radioactive element has a half-life of 5,750 years. Archeologists determined a relic had lost 25.5% of this element at the time it was found. How old is the relic? (Two steps)

2441.95 years

Step-by-step explanation:

We can model this exponencial function as:

P = Po * (1+r)^(t/n)

Where P is the final value, Po is the inicial value, r is the rate, t is the time and n is the period of half-life.

In this case, we have that P/Po = 100% - 25.5% = 74.5% = 0.745, r = -0.5 and n = 5750, so we have that:

0.745 = (1 - 0.5)^(t/5750)

Step 1: log in both sides:

log(0.745) = (t/5750) * log(0.5)

Step 2: isolate t

t = 5750*log(0.745)/log(0.5) = 2441.95 years