A science fiction enthusiast has figured out how to make nanobots with a mass of onehuman...

A science fiction enthusiast has figured out how to make nanobots with a mass of onehuman cell (10⁻¹² kg). Each nanobot is capable of reproducing itself with any material it finds at a rate of 1 nanobot per hour.
1. Assuming unlimited materials and starting with one nanobot, how many nanobotsdo we have after 10 days? What is the combined mass of those nanobots?
2. What is the general function, in terms of time t in units of hours, that tells us how many nanobots we have? Assume that at t = 0, we have one nanobot.
3. How long would it take to convert an average car into all nanobots starting witha single nanobot? How many nanobots would that be and what would their total mass be?
4. How long would it take to convert the entire Earth into nanobots? Assume anEarth mass of 6 × 10²⁴ kg.
5. How long would it take to convert the entire observable Universe into nanobots? Assume the mass of the observable Universe is 3 × 10⁵² kg and ignore travel time and energy considerations.

Expert Solution

genius_generous answered 11 months ago

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