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.
1. To calculate the number of offspring produced for each generation, we can set up a table:
Generation | Number of Pairs | Offspring per Pair | Total Offspring
---------------------------------------------------------------
1 | 1 | 6 | 6
2 | 6 | 6 | 36
3 | 36 | 6 | 216
4 | 216 | 6 | 1296
5 | 1296 | 6 | 7776
Therefore, for 5 generations, the total number of offspring produced would be 7776.
2. Graphically, the rabbit population growth would show exponential growth. On the x-axis, you would have the generations (1, 2, 3, 4, 5), and on the y-axis, you would plot the population size (6, 36, 216, 1296, 7776). The graph would show a steep increase in population size over time, indicating exponential growth.
1. To find out how many offspring would be produced each year for 5 generations, we can use the information given - a pair of rabbits produces six offspring: 3 males and 3 females. Each pair of rabbits breeds only once, and we assume that no offspring die.
For each pair of rabbits, we know that they produce 6 offspring in total. Out of these 6 offspring, 3 are males and 3 are females. This means that each pair of rabbits produces 3 more pairs of rabbits.
In the first generation, we start with 1 pair of rabbits. This pair will produce 3 additional pairs of rabbits, so we will have a total of 4 pairs in the first generation.
In the second generation, each of the 4 pairs will produce 3 more pairs, resulting in 4 * 3 = 12 pairs of rabbits.
In the third generation, each of the 12 pairs will produce 3 more pairs, resulting in 12 * 3 = 36 pairs of rabbits.
We can continue this pattern for each subsequent generation. In each generation, the number of pairs will be multiplied by 3.
Therefore, the number of offspring produced in each generation for 5 generations would be:
1st generation: 4 pairs
2nd generation: 12 pairs
3rd generation: 36 pairs
4th generation: 108 pairs
5th generation: 324 pairs
2. To construct a graph of the data, we can plot time on the x-axis (number of years) and population on the y-axis (number of pairs of rabbits). The graph will show how the rabbit population grows over time.
Given the information above, we can plot the following points on the graph:
(1, 4)
(2, 12)
(3, 36)
(4, 108)
(5, 324)
The graph will show an exponential growth pattern, where the population increases rapidly as each generation produces more offspring. The population will continue to grow at an accelerating rate over time.