The radioactive element carbon-14 has a half-life of 5750 years. a scientist determined that the bones from a mastodon had lost 60.5% of their carbon-14. how old were the bones at the time they were discovered?

7705.43 years.

Step-by-step explanation:

Let us assume that initial amount of mastodon was 1.

We have been given that the radioactive element carbon-14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost 60.5% of their carbon-14.

We will half life formula to solve our given problem.  

, where,

A= Final amount left after t years,

a = Initial amount,

t = time,

h = Half-life of substance.

Since the bones from a mastodon had lost 60.5% of their carbon-14, so amount of carbon-14 left would be:

Upon substituting our given values in half'life formula, we will get:

Upon taking natural log of both sides, we will get:

Using log property , we will get:

Now, we will divide both sides of our equation by .

Switch sides:

Therefore, the bones were approximately 7705.43 years old when they were discovered.

the first one is x^2+2x+2

the second one is x^2+4

the last one is x^2-4x+8