In the attached file is an image of a table displaying x-values of "age" and y-values of "400-meter dash times". The task is to find an equation that models the data, and through calculus (e.g....

In the attached file is an image of a table displaying x-values of "age" and y-values of "400-meter dash times". The task is to find an equation that models the data, and through calculus (e.g. derivative) will be able to find when the "400-meter dash time" will be below 45.25 seconds.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The table gives the time taken to complete a 400 m dash as a function of the age. To determine an equation that  accurately models the data an option is use software like MS Excel. 

The graph has been plotted in the figure below and it can be seen that the equation is not linear. How accurately the equation models the data depends on the highest degree of the term x in the trendline's equation. A degree 4 equation is quite accurate and is: y = -0.0018x^4 + 0.1504x^3 - 3.7756x^2 + 32.255x + 3.8377

Forecasting values of y for higher values of x by extrapolation, shows that the value of y does not go below 42.25. The lowest value of function is for a value of x close to 18. The following values of y are higher.

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