Ib Math Portfolio Type 2
Introduction
In this task, I will develop model functions representing the tolerance of human beings to G-force over time.
In general, humans have a greater tolerance to forward acceleration than backward acceleration, since blood vessels in the retina appear more sensitive in the latter direction.
As we all know, the large acceleration is, the shorter time people can bear. Using the data shown in the task and Mat lab analysis, we can get several model functions to represent the tolerance of human beings to G-force over time. Then the model functions are improved through further investigation. The validation result shows that the models represented are efficient for the tolerance of human beings to G-force over time.
Problem formulation
To define appropriate variables and parameters, and identify any constraints for the data and use technology plot the data points on a graph. Comment on any apparent trends shown in the graph. Find function to model the behavior of the graph and explain the reason to choose the function. Create an equation to fit the graph. On new set axes, draw the model function and the function of the original data points. Comment on any differences and revise the model if necessary. Discuss the implications of the model in terms of G-force acting on human beings. Use technology to find another function to model the data. On a new set of axes, draw the model function and comment on the differences. Then, check whether the first model fits the new data. Make any changes to the model if it is needed. Discuss the limitation of the model and implication in terms of G-force.
Solving problem
Define the variables and parameters, we choose t as the time human beings could tolerant and g as the acceleration. The constraints of data are as follows:
Because t must be a positive number, when g is positive number it means a forward acceleration, if g is a negative number, it represent a backward acceleration.
Using Mat lab, we plot
In this task, I will develop model functions representing the tolerance of human beings to G-force over time.
In general, humans have a greater tolerance to forward acceleration than backward acceleration, since blood vessels in the retina appear more sensitive in the latter direction.
As we all know, the large acceleration is, the shorter time people can bear. Using the data shown in the task and Mat lab analysis, we can get several model functions to represent the tolerance of human beings to G-force over time. Then the model functions are improved through further investigation. The validation result shows that the models represented are efficient for the tolerance of human beings to G-force over time.
Problem formulation
To define appropriate variables and parameters, and identify any constraints for the data and use technology plot the data points on a graph. Comment on any apparent trends shown in the graph. Find function to model the behavior of the graph and explain the reason to choose the function. Create an equation to fit the graph. On new set axes, draw the model function and the function of the original data points. Comment on any differences and revise the model if necessary. Discuss the implications of the model in terms of G-force acting on human beings. Use technology to find another function to model the data. On a new set of axes, draw the model function and comment on the differences. Then, check whether the first model fits the new data. Make any changes to the model if it is needed. Discuss the limitation of the model and implication in terms of G-force.
Solving problem
Define the variables and parameters, we choose t as the time human beings could tolerant and g as the acceleration. The constraints of data are as follows:
Because t must be a positive number, when g is positive number it means a forward acceleration, if g is a negative number, it represent a backward acceleration.
Using Mat lab, we plot