Complete the stranded time traveler's diary entry.

If my temporal calculations are correct, by the time the rescue squad finally reaches me in 2080, I ________ on this barren asteroid for precisely five decades.

The correct answer is will have been living.

We use the future perfect continuous (will have been + verb-ing) to project ourselves forward in time and look back at the duration of an ongoing action. The phrase "for precisely five decades" requires the perfect continuous aspect, eliminating "will be living."

"Would have been living" is used for unreal past conditions (third conditional), and "must have lived" is a deduction about the past.