Can Prayer Change God's Mind?

We had a discussion at the men's bible study recently regarding the power and purpose of prayer. If God already knows what is going to happen and ordains (either permissively or by direct cause) all that comes to pass, why pray? What does prayer accomplish? What, for example, can it mean when the bible describes God as "repenting" or "relenting" or changing his mind in response to faithful prayer? RC Sproul provides a great answer here:

When the Bible describes God for us, it uses human terms, because the only language God has by which to speak to us about himself is our human language. The theological term for this is anthropomorphic language, which is the use of human forms and structures to describe God. When the Bible talks about God’s feet or the right arm of the Lord, we immediately see that as just a human way of speaking about God. But when we use more abstract terms like repent, then we get all befuddled about it.

There’s one sense in which it seems God is changing his mind, and there’s another sense in which the Bible says God never changes his mind because God is omniscient. He knows all things from the beginning, and he is immutable. He is unchanging. There’s no shadow of turning within him. He knows what Moses is going to say to him before Moses even opens his mouth to plead for these people. Then after Moses has actually said it, does God suddenly changes his mind? He doesn’t have any more information than he had a moment before. Nothing has changed as far as God’s knowledge or his appraisal of the situation.

What in Moses’ words and actions would possibly have provoked God to change his mind? I think that what we have here is the mystery of providence whereby God ordains not only the ends of things that come to pass but also the means...read more