Multiplying Rabbits
Suppose that a pair of rabbits produces six offsrping: 3 males and 3 females. Assumes that no offspring die.
1. If each pair of rabbits breeds only once, how many offspring would be produced each year for 5 generations?
2. Construct a graph of your data. Plot time on the x-axis and population on the y-axis. What type of growth is the rabbit population going through after 5 years? (I just want to know how it would look like)
If there are 6 offspring, with 3 male and 3 female, then there are 3 pairs. If each pair produces 6 offspring then there will be 18. That then makes 9 pairs. That would be 54 rabbits or 27 pairs. If each of the 27 pairs produce 6 offspring there would be 162 offspring. This would leave 81 breeding pairs, which would make a total of 486 rabbits in the 5th generation.
calculate if each pair of rabbits breeds only once, how many offspring would be produced each year for five generations?
interpret Graphs construct a graph of your data. Plot time on the x-axis and population on the y-axis. What type if growth is the rabbit population going through after 5 years?
1. Well, if each pair of rabbits breeds only once, they would produce six offspring in the first generation. Then each offspring pair would breed once, resulting in six offspring per pair for a total of 12 rabbits in the second generation. Following this pattern, each subsequent generation would double the number of rabbits from the previous generation. So for 5 generations, we would have:
1st generation: 6 offspring
2nd generation: 12 offspring
3rd generation: 24 offspring
4th generation: 48 offspring
5th generation: 96 offspring
2. As for the graph, imagine a line starting at 6 and then doubling at each subsequent generation: 12, 24, 48, 96. It would be an exponential growth curve, showing the rabbit population multiplying like, well, rabbits! It would look like a steep upward slope on the graph, resembling a bunny hopping up a hill. But don't worry, they won't multiply forever... we hope.
To solve this problem, we need to understand the basic principle of rabbit reproduction and use it to calculate the number of offspring produced each year for 5 generations.
1. If each pair of rabbits breeds only once, the number of offspring produced each year can be calculated as follows:
- In the first generation, we have one pair of rabbits, which produces 6 offspring.
- In the second generation, each of the 6 offspring becomes a pair of rabbits, resulting in a total of 6 pairs. Each pair then produces 6 offspring, resulting in a total of 6 x 6 = 36 offspring.
- In the third generation, each of the 36 offspring becomes a pair of rabbits, resulting in a total of 36 pairs. Each pair then produces 6 offspring, resulting in a total of 36 x 6 = 216 offspring.
- Continuing this pattern, in the fourth generation, we would have 216 pairs of rabbits, producing 216 x 6 = 1296 offspring.
- In the fifth generation, we would have 1296 pairs of rabbits, producing 1296 x 6 = 7776 offspring.
So, for 5 generations, the total number of offspring produced would be 6 + 36 + 216 + 1296 + 7776 = 9510.
2. To construct a graph showing the population growth of the rabbit over time, we would plot time on the x-axis and population on the y-axis. Based on the calculations above, the population growth would increase exponentially with each generation. In the first generation, the population is 6. In the second generation, it becomes 36. In the third generation, it becomes 216. In the fourth generation, it becomes 1296. And in the fifth generation, it becomes 7776.
Thus, the graph would show an upward curve, starting with a small population and rapidly increasing over time. This indicates exponential growth in the rabbit population.