I’m sure you know this is an exponential growth question but have no intuition of the answer.
As per your intuition, how many seconds later will you hit 10% of c?
Let's say you have infinite ships traveling at light speed originating from earth trying to colonize the entire universe.
All of this is funded by borrowing capital from earth and earth expects a 5% annual return in perpetuity.
The space ships must pay interest to earth and if they fail to pay it, they are not allowed to perform further colonization.
Will earth manage to colonize the entire universe? Aka, can the infinite number of at light speed traveling ships outrun the interest payments?
After answering that question this one should be easy:
What if the universe was infinitely large and infinite growth was possible?
Knowing exponents and how to apply it is not the same as having any intuition about what the actual value of a certain exponential function will be at a certain point and when it crosses a threshold.