Each plant of a certain variety yields 50 seeds in the early fall and then dies. Only 40 percent of these seeds produce plants the following summer and the remainder never produce plants. At this rate, a single plant yielding seeds in 1986 will produce how many plants as descendants in 1989?
.4 * 50 = 20
20 + 20^2 + 20^3 + 20^4 = ?
To determine the number of plants as descendants in 1989, we need to consider the steps involved.
First, let's start with a single plant that yields 50 seeds in 1986. Since only 40% of these seeds produce plants the following summer, we can calculate the number of plants from those seeds.
40% of 50 seeds: 50 * 0.4 = 20 plants
Therefore, from one plant in 1986, we have 20 new plants in 1987.
Now, in 1987, each of these 20 plants will follow the same pattern: yield 50 seeds in the early fall. Again, only 40% of these seeds will produce plants the following summer. So, we need to calculate the number of plants from these 20 plants in 1987.
40% of 20 plants: 20 * 0.4 = 8 plants
Therefore, from the 20 plants in 1987, we have 8 new plants in 1988.
Lastly, in 1988, each of these 8 plants will yield 50 seeds, and once again, only 40% of these seeds will produce plants the following summer. So, we need to calculate the number of plants from these 8 plants in 1988.
40% of 8 plants: 8 * 0.4 = 3.2 plants
Since we cannot have a fraction of a plant, we can round this down to 3 plants.
Therefore, from the 8 plants in 1988, we have 3 new plants in 1989.
Adding up all the plants at each stage:
Initial plant in 1986: 1 plant
Plants in 1987: 20 plants
Plants in 1988: 8 plants
Plants in 1989: 3 plants
Thus, a single plant that yields seeds in 1986 will have 3 plants as descendants in 1989.