Why did Peter and the eleven continue the same miracles and ministry that Jesus and the twelve had done?
Peter and the eleven continued those miracles as an extension of Christ's earthly ministry to the same audience, the nation of Israel. Their miracle-working power was meant to convince Israel that Jesus was who He claimed to be and would still fulfill His promises if the nation believed.
Les explains that after the Holy Spirit came upon them, they were to receive power, specifically miracle-working power, so they would be an extension of Christ's earthly ministry. Everything Jesus and the twelve had performed in those three years, Peter and the eleven were to continue, because they were dealing with the same people: the nation of Israel. They were trying to convince the nation that Jesus was who He said He was and was still going to fulfill His promises if they would simply believe. So they continued with signs and wonders, meeting with one accord in Solomon's Porch at the Temple, still taking sacrifices and practicing Judaistic ritual. The only thing added was that they had believed Jesus was whom He said He was. Les also notes that archeologists are finding evidence of first- and second-century Jews who practiced Judaism while embracing Jesus of Nazareth as the Messiah.