could you help

Let Y denote the waiting time in years between two global pandemics, which has an exponential distribution Y ~ Exp(A), where A is the rate parameter. The data includes n observations (31 , y/2, . . . , yn). . Prove that Gamma(r, v) is a conjugate prior for A . . Derive the posterior mean of A (The proof is required). Hint: use the gamma function, I(c) = (c - 1) * I(c -1) whether or not c is an integer