Matthew 28:19 says:
Go ye therefore, and teach all nations, baptizing them in the name of the Father, and of the Son, and of the Holy Ghost:
This was the last commandment Jesus gave to his disciples before he ascended into heaven at the end of his earthly ministry. His restored church, the Church of Jesus Christ of Latter-day Saints has worked hard to keep this commandment, and has been quite successful. I do not base my testimony on how rapidly the Church is growing but I do find the world-wide growth of the Church fascinating and fulfillment of prophecy.
To better visualize how the Church has expanded into new places I made a timeline video map showing when each US state and each nation or territory outside the US got its first stake and its first temple. This video does not show nations or territories with missions, districts or branches but no stake or temple yet. So the Church has a presence in many places beyond those shown.
To simplify things I used a map with current political boundaries.
A location turns yellow when it has its first stake.
A location turns green when it has a temple but no stake (see below).
A location turns red when it has both a stake and a temple.
With four, soon to be five, exceptions the Church has only built temples in places that already had a stake. These locations turn green when they have their first temple and then red when they have both a stake and a temple. The exceptions are:
Hawaii which had its first temple in 1919 and its first stake in 1935,
Switzerland which had its first temple in 1955 and its first stake in 1961,
New Zealand which had its first temple April 1958 and its first stake in May 1958 and
Great Britain which had its first temple 1958 and its first stake in 1960.
Additionally the Church has announced a temple for Shanghai China though there are no stakes in China yet.
As one would expect the Church did not expand much in its early years. Once the saints reached Utah they stayed within Utah for a couple of decades before they began to expand into new states, nations and territories. This reflects the Church's early focus on having saints gather to Utah during the pioneer period and then later to build up Zion in the saint's homelands.
The Church has not and will not grow at a constantly high rate. I see the administration of the Church as analogous to my own life. I face opposition, suffer setbacks and make mistakes, I even sin. The Church is no different, its organization is perfect but its administration is not. It is led by prophets but they are still men. The inspiration they receive comes line upon line. They have to work to learn and understand the will of the Lord. They also have to figure out how to find and touch the hearts of individuals from a huge range of cultures, backgrounds and life situations. The Lord doesn't tell them how to do this but he does give them the tools to figure it out, eventually. Everything happens according to the Lord's will and timetable, and no one, not even the Prophet completely understands His will.
The Church will eventually fill the whole earth as prophesied in Daniel 2:34-35. but it will take time, there will be setbacks, opposition and even mistakes along the way.