The radioactive element carbon- 14 has a half-life of 5750 years. A scientist determined that the bones from a mastodon had lost $844 \%$ of their carbon-14. How old were the bones at the time they were discovered? The bones were about years old (Round to the nearest integer as needed)

Step 1 ：\(\text{Let } n \text{ be the number of half-lives that have passed.}\)

Step 2 ：\(\text{After } n \text{ half-lives, the remaining carbon-14 is } (0.5)^n \)

Step 3 ：\(\text{Since the bones have lost } 844\% \text{ of their carbon-14, they have } 100\% - 844\% = -744\% \text{ remaining.}\)

Step 4 ：\(\text{So, } (0.5)^n = -7.44 \)

Step 5 ：\(\text{Taking the natural logarithm of both sides, we get } n \ln(0.5) = \ln(-7.44) \)

Step 6 ：\(\text{Solving for } n, \text{ we get } n = \dfrac{\ln(-7.44)}{\ln(0.5)} \)

Step 7 ：\(n \approx 2.999 \)

Step 8 ：\(\text{The age of the bones is } n \times \text{half-life} = 2.999 \times 5750 \)

Step 9 ：\(\text{The age of the bones is } \approx 17244 \text{ years}\)

Step 10 ：\(\boxed{17244}\)