Chapter 12, Problem 18CT

a.

To determine

To find the quadratic model using the regression feature of graphing calculator.

Answer to Problem 18CT

  $y=8.786x^2-6.243x-0.428$ .

Explanation of Solution

Given:

The given table shows the altitude $y$ in feet of a space shuttle during the first $5$ seconds of motion.

  

Calculation:

  

The required function is $y=8.786x^2-6.243x-0.428$

b.

To determine

To find the velocity of the shuttle at $x=5$ seconds.

Answer to Problem 18CT

  $81.617\text{ feet/second}$ .

Explanation of Solution

Given:

The given function is

  $f(x)=2x^3-x^2-10x+5$

Calculation:

Substituting the value $x=5$ in the derivative of the equation $y=8.786x^2-6.243x-0.428$

  $\begin{array}{l}y=8.786x^2-6.243x-0.428\\ y^{\text{'}}=17.572x-6.243\end{array}$

Thus velocity of the shuttle at $x=5$ seconds is −

  $\begin{array}{l}{f}^{\text{'}}(5)=17.572x-6.243\\ f^{\text{'}}(5)=17.572(5)-6.243\\ f\text{'}(5)=81.617\text{ feet/second}\end{array}$