Chapter 4.9, Problem 16E

To determine

To calculate: The polynomial model of function using the given values and the age of human if cat’s age is $3$ .

Answer to Problem 16E

The required cubic function is $f\left(x\right)=0.0958328x^3+1.52587x^2+11.4246x-5.4791$ and the age of human is $28.6$ 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.

  $0.0958328x^3+1.52587x^2+11.4246x-5.4791$

Represent the above equation in terms of function.

  $f\left(x\right)=0.0958328x^3+1.52587x^2+11.4246x-5.4791$

Substitute $3$ for x in the above equation.

  $\begin{array}{c}f\left(x\right)=0.0958328x^3+1.52587x^2+11.4246x-5.4791\\ =0.0958328\times 3^3+1.52587\times 3^2+11.4246\times 3-5.4791\\ =28.6\end{array}$

Hence, the required cubic function is $f\left(x\right)=0.0958328x^3+1.52587x^2+11.4246x-5.4791$ and the age of human is $28.6$ years.