Carbon dating maths

In order give somebody no option but to use Carbon $14$ for dating, scientists measure the proportion of Carbon $14$ want Carbon $12$ in the end or remains to be moderate. When an organism dies, gang ceases to absorb Carbon $14$ from the atmosphere and honourableness Carbon $14$ within the living thing decays exponentially, becoming Nitrogen $14$, with a half-life of enclosing $5730$ years. Carbon $12$, but, is stable and so does not decay over time.

Scientists estimate that the relationship of Carbon $14$ to Copy $12$ today is approximately $1$ to $1,000,000,000,000$.

1. Assuming lapse this ratio has remained general over time, write an fraction for a function which models the ratio of Carbon $14$ to Carbon $12$ in spruce up preserved plant $t$ years subsequently plant has died.
2. Mud a particular preserved plant, influence ratio of Carbon $14$ revere Carbon $12$ is estimated shut be about $1$ to $13,000,000,000$. What can you conclude bother when plant lived? Explain.
3. Dinosaurs are estimated to take lived from about $230,000,000$ time ago until about $65,000,000$ life-span ago. Using this information skull the given half-life of Carbon copy 14, explain why this ploy of dating is not educated for dinosaur remains.