Question

Find a growth rate such that the time complexity is squared whenever the instance size is doubled. In other words, if t(n) = x, then t(2n) = x². What is the growth rate?

Answer 1

In order for the time complexity to be squared whenever the instance size is doubled, the growth rate must be exponential.

Step-by-step explanation:

In order for the time complexity to be squared whenever the instance size is doubled, the growth rate must be exponential. Exponential growth is characterized by a constant growth rate, where the scale increases by a factor of the base raised to the number of doubling times.

For example, if we start with t(n) = 1 and double the instance size to t(2n), the growth rate would be t(2n) = (t(n))².

Therefore, the growth rate is exponential.