Debbie, it must be an anxious time. Those are big PSA rises.
As Ohwow says, at 89 they will want to consider how your father would respond to any radical treatment. It is quite likely hormone treatment (blocking testosterone, on which most prostate cancers depend) would be considered but the side effects and (probably) long recovery time from surgery or radiotherapy might rule those out.
Good luck for tomorrow. It is reasonable for your father to make a choice about biopsy if he wants, to be honest a scan to see if there are metastases seems more relevant (if there are multiple metastases that might rule out surgery and radiotherapy anyway, but hormone treatment should still be effective).