# SL Type II Mathematics Portfolio

G-Force Tolerance

SL Type II Mathematics Portfolio

G-force, measured in (g), is a force that acts on a body as a result of acceleration or gravity. Human tolerances of the g-force are depending on the magnitude of the g-force, and the length of time it is being applied, the direction it acts, and the location of application. The human body has a better chance at surviving horizontal g-force. Horizontal g-force is referred as “eyeballs-in”. Vertical acceleration upwards is referred to as “blood towards feet”. Research shows that humans have a much high tolerance for “eyeballs-in” than any other g-forces. The standard 1g on the Earth’s surface is caused by gravity, and to prevent humans from free-falling. As the G-forces increases, the time that a human can tolerate it significantly decreases.

Human Tolerance vs. Horizontal G-force

From the examination of human tolerance to horizontal G-force, a model function will be developed to represent the relationship between them. This portfolio will be focused on creating a function that best suits the table of value above.

It is clear that +Gx, measured in gravity (g), is the independent variable in this case as it is affecting the time humans can tolerate. Thus, we can let  horizontal G-force. Consequently, the dependent variable in this case would be the time in which humans can tolerate, measured in minutes (min.) This is due to the fact that the amount of time humans can tolerate is dependent of the G-force itself; therefore . The notation in which the function would model after is. We set that  because this function would only be applied to positive G-Force. Another constraint is that  because the human tolerance time has to be at a value which we can measure.

When table of values are plotted on a graph, it is clear that as the horizontal G-forces increase, the time would quickly decrease as a consequence. Another trend shown in this graph is that as the G-forces decrease, the time would increase as the result.

By observing the data above, it resembles the graph. We can see that as is approaching positive infinity, the values of y is approaching zero from above. (). This is also true as  is approaching zero from the positive, the values of  is approaching positive infinity. The 2 primary traits of , fits well with the plotted data. Thus, the function model I have decided to use is. The vertical asymptote and the horizontal asymptote in this case are both 0, because this graph never crosses or touches the There is no visible vertical or horizontal translation, thus, the -value and the -value are 0. The two parameter in this case is  and, and their purpose will be listed below:

The  value serves as a scaling factor for this function. By moving the value of  up or down will result in a vertical stretch or vertical compression, respectively.

The  value determines the function’s rate of growth or decay. The  value can alter the function’s overall shape and behaviour.

The power functions of 2 points can be solved by using substitution. It can be done by first isolating the  value, and then substitute the  value in the second equation to solve for the value. After that, substitute the  value in the first equation to get a  value. This can ...