Homework - Functions and Control Flows

Last year, a mammoth's femur was found under Reser Stadium, and it is said that Manny's femur is at least 10,000 years old. However, to determine the age of the femur, scientist would want to perform a radiocarbon (¹⁴C) dating analysis. The governing equation for such analysis is:

N(t) = N₀e^-λt

where N₀(t = 0) is the initial number of radiocarbon atoms, N is the number of atoms present today, λ is the decay constant of radiocarbon, and t is time. It is also known that the relationship between the number of atoms and activity is:

A = λN

λ = Ln2/t_1/2

For this assignment you are asked to create a function with the following properties:

The function you create should work whether I provided 2 or 4 different input variables and the default output variable is N, i.e., if I only give one output variable it should return the number of atoms present today. Nonetheless, if two are provided, the function should return N; t_1/2; Activity if I call for the other variables. If I provide 4 input variables, then it should return the decay plot up to today of any of the string options, i.e., if 'Activity' plot activity. After completing the function:

1. If the initial number of (¹⁴C) atoms is 10²⁰, how many atoms are there today? What is the activity that should be found in the sample if it has decay for 10,000 years? What is the half-life of (¹⁴C)?

2. Create a vector with Options variable, i.e., Activity, NumAtoms, Both, and create a for loop that calls for your function such that it returns each of the following plots:

• Plot of number of atoms over 10,000 years
• Plot of activity over 10,000 years
• Plot of both the activity and number of atoms over 10,000 years