The third situation in which silence is acceptance occurs when (1) the offeror gives the offeree reason to assume that silence will constitute acceptance of the offer; and (2) the offeree remains silent with the intent of thereby accepting the offer. Restatement (Second) Contracts ยง 69(1)(b).
By way of illustration, suppose Jacob has been using Ralph's computer, which Ralph lent him for a month free of charge. Before the month is over, Ralph writes a letter to Jacob in which he offers to sell him the computer for $300; Ralph adds, "I am quite certain you will accept, so if I do not hear from you to the contrary, I will assume you do."
Jacob does not respond to the letter at all. He just remains silent.
Jacob accepted Ralph's offer only if he intended by his silence to do so.
If Jacob did not intend his silence to be acceptance, he should have notified Ralph of that fact.