Final answer:
Without specific data points for stalactite samples' age and length, we cannot identify which provided linear equation is correct. A linear regression analysis could be used by researchers to determine the most accurate model based on actual measurements of stalactites.
Step-by-step explanation:
To determine a linear model that expresses length as a function of age for stalactites in a cave, researchers would use a formula that correlates the estimated age to the length of sample stalactites. The options provided are all in the form of a linear equation represented by Length = ax + b, where a is the growth rate per thousand years, and b is the length at time zero or the y-intercept.
Since we are not given the specific data points to create the linear model, we can not definitively identify which provided equation is accurate. However, if the researchers have data on the age and length of multiple stalactite samples, they can use regression analysis to find the best-fit line. This line will have an equation of the described form, where x is the age of the stalactite and y (or Length) is the length in micrometers.