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Question: if a robot creates another robot (which can also create another robot every 3 seconds) how many robot would there be at the end of 3 minutes
Let's break this problem down. At t=0 seconds, there is 1 robot. At t=3 seconds (1st interval), the first robot creates another robot, making a total of 2 robots. At t=6 seconds (2nd interval), both the first robot and the first-created robot each create a robot, making a total of 2 + 2 = 4 robots. At t=9 seconds (3rd interval), all 4 robots create a new robot, doubling the total to 8 robots. We can see that there is a pattern here: every 3 seconds (each interval), the number of robots doubles. There are 180 seconds in 3 minutes. Since each interval is 3 seconds long, there are 180/3 = 60 intervals in total. For each interval, the robot count doubles. So, after 60 intervals, the number of robots will have doubled 60 times: Robots = 1 * 2^60 Robots ≈ 1.15 * 10^18 Therefore, there will be approximately 1.15 * 10^18 robots at the end of 3 minutes.
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