To calculate the extent to which the expansionist civilization would have colonized the Andromeda galaxy, we need to consider the time elapsed and the maximum speed of expansion. Given: - Time elapsed since the civilization emerged: 2 billion years (2 x 10^9 years) - Maximum speed of expansion: 5% of the speed of light (0.05c) To determine how far the civilization could have expanded in this time, we can use the formula for distance traveled: Distance = Speed x Time The distance traveled by the civilization can be calculated as follows: Distance = (0.05c) x (2 x 10^9 years) However, it is important to note that we should convert the time from years to seconds and the speed from the speed of light to meters per second to obtain consistent units. 1 year = 365.25 days * 24 hours * 60 minutes * 60 seconds = 31,557,600 seconds Speed of light (c) = 299,792,458 meters per second Therefore, the distance traveled by the civilization in meters would be: Distance = (0.05 * 299,792,458 m/s) * (2 x 10^9 years * 31,557,600 s/year) Calculating this: Distance 0.05 * 299,792,458 * 2 * 10^9 * 31,557,600 meters This calculation yields an approximate result of: Distance 947,788 light-years Thus, the expansionist civilization would have colonized an approximate distance of 947,788 light-years within the Andromeda galaxy.

To determine how much of the Andromeda galaxy the expansionist civilization has colonized, we need to compare the distance they have traveled (947,788 light-years) with the size of the Andromeda galaxy. The Andromeda galaxy, also known as Messier 31 (M31), has an estimated diameter of about 220,000 light-years. By comparing the distance traveled by the civilization (947,788 light-years) to the diameter of the Andromeda galaxy (220,000 light-years), we can calculate the fraction of the galaxy colonized. Fraction Colonized = (Distance Traveled / Diameter of Andromeda) Fraction Colonized = (947,788 light-years / 220,000 light-years) Calculating this: Fraction Colonized 4.308 This means that the expansionist civilization, assuming they have traveled at a maximum speed of 5% of the speed of light for 2 billion years, could have potentially colonized approximately 4.308 times the diameter of the Andromeda galaxy.