Carbon-14 can yield dates of only “thousands of years” before it all breaks down.Although many people think radiocarbon dating is used to date rocks, it is limited to dating things that contain the element carbon and were once alive (like fossils).In contrast, radiocarbon forms continually today in the earth’s upper atmosphere.
If we assume Carbon-14 decays continuously, then $$ C(t) = C_0e^, $$ where $C_0$ is the initial size of the sample. Since it takes 5,700 years for a sample to decay to half its size, we know $$ \frac C_0 = C_0e^, $$ which means $$ \frac = e^, $$ so the value of $C_0$ is irrelevant.
Now, take the logarithm of both sides to get $$ -0.693 = -5700k, $$ from which we can derive $$ k \approx 1.22 \cdot 10^.
(Since this is a decay problem, I expect the constant to be negative.
If I end up with a positive value, I'll know that I should go back and check my work.) In Its radiation is extremely low-energy, so the chance of mutation is very low.
However, I note that there is no beginning or ending amount given.
How am I supposed to figure out what the decay constant is?
CARBON-14 IS ABSORBED (Figure 1b): Plants absorb this carbon-14 during photosynthesis.
When animals eat the plants, the carbon-14 enters their bodies.
CARBON-14 IS CREATED (Figure 1a): When cosmic rays bombard the earth’s atmosphere, they produce neutrons.