Yes, the world will sustain 7 billion people by 2045, because there is plenty of room. There is enough food for everyone in the world to eat. People starve because it is distributed poorly. Anyone who has ever driven through Iowa knows that there is plenty of room left for others. Also, engineering will help us be more efficient with the space we have.
With the birth rate rising and the modern of medical society, There is no way we will sustain 7 billion people in 2045. It seems that people are living longer and everyone is having kids. Also, the people having kids are getting younger and younger. Add those 2 together in 25 years we will be over 8 billion.