Average Rate of Change for swimming times over 100 m

[kjones]

The time it takes an average athlete to swim 100 meters freestyle at age "x" years can be modeled by:

. . .T (x) = 0.18x^2 - 8.5x + 147

where T (x) is the number of seconds for the swim.

I need to graph this function to estimate the rate at which the time is changing for a 15 year old.

I also need to find the AROC ("average rate of change") over the intervals 15, 15.1, 15, 15.01, etc.

I need some help to get started, please.

K

 

[stapel]

To graph a function, pick some x-values, plug them into the equation, find the corresponding y-values, draw the dots, and then rough in the sketch. Note: You can use your TI-83 to find the dots for you, by using the GRAPH and TABLE utilities.

Eliz.

 

[galactus]

The average rate of change is the slope of the secant line joining the points \(\displaystyle (x_{0},f(x_{0}))\;\ and\;\ (x_{1},f(x_{1}))\) on the graph.

\(\displaystyle \L\\m_{sec}=\frac{f(x_{1})-f(x_{0})}{x_{1}-x_{0}}\)

An example:

Find the average rate of change for \(\displaystyle y=x^{2}+1\) over the interval [3,5]

\(\displaystyle x_{0}=3\;\ and\;\ x_{1}=5\)

\(\displaystyle m_{sec}=\frac{f(5)-f(3)}{5-3}=\frac{26-10}{5-3}=8\)