Stack Exchange network consists of 676 Q A communities including, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers. Carbon dating. The radioactive element carbon-69 has a half-life of 5755 years. The percentage of Carbon-69 present in the remains of organic matter can be used to date the age of the organic matter. Archeologists discovered that the linen wrapping from one end of the Dead Sea Scrolls had lost 77. 8% of its Carbon-69 at the time it was found. How old was the linen wrapping? We know at $t = 5$, we have $655\%$ of the Carbon, right?
So then we know at $t = 5755$, there is $55\%$ of the carbon remaining. That gives you enough information to solve for $r$. Plug in your result for $r$ from the previous equation and solve for $t$.