Chapter 4.9, Problem 17E

To determine

To calculate: The polynomial model of function using the given values and the speed of the boat if engine’s speed is $28\text{RPM}$ .

Answer to Problem 17E

The required cubic function is $f\left(x\right)=-0.000243734x^3+0.0255245x^2-0.0242293x+2.15682$ and the speed is $16.14\text{RPM}$ years.

Explanation of Solution

Given information:

The given values are:

  

Calculation:

Consider the given values of unknown:

  

Substitute the above values in a graphing calculator.

Use the cubic regression to form the equation.

  $-0.000243734x^3+0.0255245x^2-0.0242293x+2.15682$

Represent the above equation in terms of function.

  $f\left(x\right)=-0.000243734x^3+0.0255245x^2-0.0242293x+2.15682$

Substitute $28$ for x in the above equation.

  $\begin{array}{c}f\left(x\right)=-0.000243734x^3+0.0255245x^2-0.0242293x+2.15682\\ =-0.000243734\times {24}^3+0.0255245\times {24}^2-0.0242293\times 24+2.15682\\ =16.14\end{array}$

Hence, the required cubic function is $f\left(x\right)=-0.000243734x^3+0.0255245x^2-0.0242293x+2.15682$ and the speed is $16.14\text{RPM}$ years.