Q. Could you proof this question?

Algorithm 1.7 (nth Fibonacci Term, Iterative) is clearly linear in n, but is it a linear-time algorithm? In Section 1.3.1 we defined the input size as the size of the input. In the case of the nth Fibonacci term, n is the input, and the number of bits it takes to encode n could be used as the input size. Using this measure, the size of 64 is lg 64 6, and the size of 1,024 is lg 1,024 10. Show that Algorithm 1.7 is exponential-time in terms of its input size. Show further that any algorithm for computing the nth Fibonacci term must be an exponential-time algorithm because the size of the output is exponential in the input size