a student wants to estimate the population size and density of birch trees in a woodlot measuring 100 m by 100 m. On a diagram of the woodlot, she splits the area into a 10 by 10 grid and randomly selects 10 sample quadrants - (0,0), (1,4), (2,6), (3,9), (4,3), (5,5), (6,1), (7,8), (8,2), and (9,7). These areas of the woodlot are marked off, and the birch trees are counted. She finds 15, 25, 40, 20, 10, 30, 25, 5, 15, and 35 trees in the ten quadrants. Estimate the density and size of the birch-tree population in the woodlot.
An object has a length of 5.0 cm, a height of 3.0 cm and a width of 15.0 cm. It has a mass of 24 grams. What is its density
volume= (15cm)(3cm)(5cm)=225cm^3
mass=24g
density=mass/volume
density=24/225=8/75g.cm^-3
To estimate the population size and density of birch trees in the woodlot, we can use a sampling method called quadrat sampling. In this method, a grid is placed over the area of interest, and a random selection of quadrats (grid cells) is sampled to count the number of birch trees within those quadrats.
In this case, the woodlot is 100 m by 100 m and divided into a 10 by 10 grid. The student randomly selected 10 sample quadrants: (0,0), (1,4), (2,6), (3,9), (4,3), (5,5), (6,1), (7,8), (8,2), and (9,7).
The number of birch trees counted in each of the 10 sample quadrants are as follows: 15, 25, 40, 20, 10, 30, 25, 5, 15, and 35 trees.
To estimate the density of birch trees, we need to calculate the average number of trees per quadrant. Let's sum up the number of trees in the 10 quadrants: 15 + 25 + 40 + 20 + 10 + 30 + 25 + 5 + 15 + 35 = 200 trees.
Now, divide the total number of trees by the total number of quadrants (10): 200 trees / 10 quadrants = 20 trees per quadrant.
The estimated density of birch trees in the woodlot is 20 trees per quadrant.
To estimate the size of the birch-tree population in the woodlot, we need to extrapolate the density to the entire area.
Since the woodlot is 100 m by 100 m and divided into a 10 by 10 grid, each quadrant represents an area of 10 m by 10 m.
The total area of the woodlot is 100 m * 100 m = 10,000 square meters.
Since each quadrant represents 10 m * 10 m = 100 square meters, there are a total of 10,000 square meters / 100 square meters = 100 quadrants in the woodlot.
To estimate the size of the birch-tree population, we can multiply the density (20 trees per quadrant) by the total number of quadrants (100).
20 trees per quadrant * 100 quadrants = 2000 trees.
Therefore, the estimated size of the birch-tree population in the woodlot is 2000 trees.