The original question is: Suppose a bivalve shell fragment is also found to have 76% of the amount of original 14C. In this case, after doing the analysis as in part (a), an archaeologist might subtract around 440 years from the calculated age. This is to account for the fact that deep ocean water mixing with surface water produces a reservoir effect. Your graph should be of the decay curve of 14C over time, along with intervals on the t-axis describing the “calculated age” and “actual age” of the shell fragment.
For part A I found the age of a wood fragment that had the same amount of Carbon-14 present (2270 years). However, I am really unsure as to how I would find the intervals for the age of the bivalve shell. Any help is appreciated.
$$N = {N_0}{e^{ - kt}}$$ $$k = \frac{ln(2)}{5730}$$ $$\frac{N}{{{N_0}}} = {e^{ - kt}} = {\text{fraction remaining}}$$
Just plot the fraction remaining as a function of time. Below the regular time labels, write the time values minus 440. Sort've like this... though I'm sure you can make a nicer looking graph.