A scientist has four petri dishes of different sizes. Each dish contains a different number of bacteria.
| | Population of Bacteria | Area ($mm^2$) |
| :----- | :---------------------- | :------------- |
| Dish A | 7,200 | 2,826 |
| Dish B | 10,000 | 7,850 |
| Dish C | 13,650 | 20,096 |
| Dish D | 21,350 | 31,400 |
Find each population density, to the nearest hundredth. Which statement is true?
A. Dish A has the lowest population density.
B. Dish C has the greatest population density.
C. Dish A and Dish B have approximately the same population density.
D. Dish C and Dish D have approximately the same population density.
Answer (1)
Calculate the population density for each dish by dividing the population by the area.
Round each calculated density to the nearest hundredth.
Compare the rounded densities to evaluate the given statements.
Determine that Dish C and Dish D have approximately the same population density, which is the true statement. D i s h C an d D i s h D ha v e a pp ro x ima t e l y t h es am e p o p u l a t i o n d e n s i t y .
Explanation
Understanding the Problem We are given the bacteria population and area for four petri dishes (A, B, C, and D). Our goal is to calculate the population density for each dish, round it to the nearest hundredth, and then determine which of the provided statements is true. The population density is calculated by dividing the population by the area.
Calculating Population Densities First, we calculate the population density for each dish:
Dish A: Population Density = 2826 7200
Dish B: Population Density = 7850 10000
Dish C: Population Density = 20096 13650
Dish D: Population Density = 31400 21350
Determining the Values Next, we find the values of these fractions:
Dish A: Population Density = 2.54777...
Dish B: Population Density = 1.27388...
Dish C: Population Density = 0.67923...
Dish D: Population Density = 0.67993...
Rounding to the Nearest Hundredth Now, we round each population density to the nearest hundredth:
Dish A: Population Density ≈ 2.55
Dish B: Population Density ≈ 1.27
Dish C: Population Density ≈ 0.68
Dish D: Population Density ≈ 0.68
Comparing Densities and Finding the True Statement Finally, we compare the rounded population densities to determine which statement is true:
Dish A has the lowest population density: False (Dish A has a density of 2.55, which is not the lowest).
Dish C has the greatest population density: False (Dish C has a density of 0.68, which is not the greatest).
Dish A and Dish B have approximately the same population density: False (Dish A has a density of 2.55 and Dish B has a density of 1.27, which are not approximately the same).
Dish C and Dish D have approximately the same population density: True (Dish C and Dish D both have a density of 0.68, which are approximately the same).
Examples
Population density is a useful concept in various real-world scenarios. For example, it can be used to determine how crowded a city is, or how many plants can grow in a certain area of a forest. In epidemiology, population density helps in understanding how quickly a disease might spread through a population. By calculating the number of individuals per unit area, we can better assess resource needs, environmental impact, and potential risks associated with overcrowding.
