Consider the following statement: analyzing the recurrence for a recursive algorithm usually reveals that it requires exponential time. Is this correct?

Yes $-$ recursive algorithms are always exponential time.

No $-$ it depends on the number of recursive calls that each call to the algorithm must make.

No $-$ rewriting the function to a closed form is what causes the exponential time.

Yes $-$ Towers of Hanoi is a concrete example of this.