Question

the plotted points in the graph below represent the age and vo2 max of 6 professional athletes, where vo2 max is a measure of aerobic fitness. the function ( y = -0.3x^{2}+18x - 200 ) has been fitted to model the relationship between age and vo2 max. according to the model, what will be the vo2 max of an athlete when they retire at the age of 38?

Explanation:

Step1: Substitute \(x = 38\) into the function

Given the function \(y=-0.3x^{2}+18x - 200\), when \(x = 38\), we have \(y=-0.3\times(38)^{2}+18\times38-200\).
First, calculate \((38)^{2}=38\times38 = 1444\). Then \(-0.3\times(38)^{2}=-0.3\times1444=-433.2\).
Next, calculate \(18\times38 = 684\).

Step2: Calculate the value of \(y\)

Now, substitute these values back into the function: \(y=-433.2 + 684-200\).
\(y=( - 433.2+684)-200\).
\(-433.2 + 684=250.8\).
Then \(y=250.8-200\).

Answer:

\(y = 50.8\)