Final answer:
The growth rate that meets the condition where time complexity is squared when the instance size is doubled is a quadratic growth rate, such as an^2 + bn + c. This relationship naturally scales the initial time complexity function by a factor of four when the input size is doubled, satisfying the given condition.
Step-by-step explanation:
The student is asking about a specific type of growth rate in the context of time complexity, where the growth rate is such that when the size of an instance is doubled, the time complexity becomes squared. The question is essentially asking for a growth rate that adheres to the equation t(2n) = (t(n))^2, where t(n) represents the time complexity function for an instance of size n.
To fulfill this condition, the growth rate must be quadratic. This means that t(n) can be a function like an^2 + bn + c, where a, b, and c are constants. When the input size doubles, i.e., for t(2n), this function becomes 4an^2 + 2bn + c. This quadratic relationship naturally results in the time complexity being squared relative to the original input size.
The exponential growth mentioned in the information is slightly different but can be used to explain similar concepts in a real-world context, such as population growth, where the size doubles over constant time intervals. The provided rule of 70 is a quick way to estimate doubling time for small percentage growth rates. However, for the question at hand, a quadratic growth rate is more appropriate and directly answers the student's query.