An experiment with results acquired showed that at the beginning the temperature was 20 degrees and the size of bacteria was 1 mm long. 12 hours later the temperature was 56 degrees and the size of the bacteria was 12 mm long. Create a graph showing the size of the bacteria along with the temperature and find a mathematical relation between both variables
To create a graph showing the relationship between the size of the bacteria and the temperature, you can use a scatter plot. The x-axis will represent the temperature, and the y-axis will represent the size of the bacteria.
Here is the data we have:
Initial temperature: 20 degrees Celsius
Initial size of bacteria: 1 mm
Temperature after 12 hours: 56 degrees Celsius
Size of bacteria after 12 hours: 12 mm
To find the mathematical relationship between these variables, we can use linear regression to determine if there is a linear correlation between temperature and size.
First, let's calculate the change in temperature:
Temperature change = Final temperature - Initial temperature
Temperature change = 56°C - 20°C = 36°C
Next, let's calculate the change in size:
Size change = Final size of bacteria - Initial size of bacteria
Size change = 12 mm - 1 mm = 11 mm
Now, we can calculate the rate of change of size with respect to temperature:
Rate of change = Size change / Temperature change
Rate of change = 11 mm / 36°C
The mathematical relation between the size of the bacteria and the temperature can be approximated as:
Size of bacteria = (Rate of change) * Temperature + Initial size of bacteria
Plugging in the values:
Size of bacteria = (11 mm / 36°C) * Temperature + 1 mm
Now, let's plot the graph using the given data points and the equation.
(x-axis: Temperature, y-axis: Size of bacteria)
(20°C, 1 mm)
(56°C, 12 mm)
By plotting these points and drawing a line or curve that best fits the data, we can visualize the size of the bacteria as a function of temperature.