Final answer:
Tania's chain letter process can be described recursively as T(n) = 4 * T(n - 1), which means each day's total is four times the total of the previous day. It can also be described by the explicit formula, T(n) = 4^n, an exponential function representing the number of letters sent on the nth day.
Step-by-step explanation:
The student's question involves a scenario where Tania creates a chain letter and sends it to four friends. Each day, every person who has the letter is instructed to send it to four more friends. This scenario can be explained using concepts of recursive sequences and explicit formulas in mathematics, specifically in the topic of exponential growth.
RECURSIVE ASPECT
The recursive aspect of this process refers to the way the number of letters sent can be determined based on the previous day's count. On day 1, Tania sends out 4 letters. We denote this as T(1) = 4. For every subsequent day n, the total number of letters sent, denoted as T(n), can be calculated by multiplying the previous day's total by 4, which can be written as T(n) = 4 * T(n - 1). This is the recursive formula.
EXPLICIT ASPECT
The explicit aspect refers to a formula that can calculate the number of letters sent on any given day n without the need to know the previous day's count. This can be determined using the initial value and the rate of growth. The explicit formula is T(n) = 4^n, where the exponent represents the number of days since the initial letter was sent by Tania. This shows the pattern of exponential function which represents how rapidly the chain letter spreads.