Final answer:
The formula for a quantity y doubling every T unit of time is y(t) = y' * 2^(t / T), where y' is the initial amount and t is the elapsed time. This represents the mathematical concept of exponential growth.
Step-by-step explanation:
Exponential Growth
The student's question is referring to a mathematical concept known as exponential growth, where a quantity increases or 'grows' at a rate proportional to its current value. In this context, where quantity y doubles every T units of time, the formula you're looking for is y(t) = y' * 2^(t / T), where:
- y is the quantity after t units of time,
- y' is the initial amount,
- t is the elapsed time in the same units as T,
- T is the doubling period in the same units as t.
In this formula, '2' is the base of the exponential, representing the doubling nature of the growth, while '(t / T)' is the exponent, indicating how many doubling periods 'T' has passed in the elapsed time 't'.
Learn more about Exponential Growth