Question

Identify the polynomial that can be used to model the total cost.

Answer 1

Solution:

Given:

$\begin{gathered} h(x)=0.42x^2+0.3x+4 \\ r(x)=-0.005x^2-0.2x+7 \end{gathered}$

Hence, the total cost is;

$\begin{gathered} q(x)=h(x)\cdot r(x) \\ q(x)=(0.42x^2+0.3x+4)(-0.005x^2-0.2x+7) \\ q(x)=0.42x^2(-0.005x^2-0.2x+7)+0.3x(-0.005x^2-0.2x+7)+4(-0.005x^2-0.2x+7) \\ q(x)=-0.0021x^4-0.084x^3+2.94x^2-0.0015x^3-0.06x^2+2.1x-0.02x^2-0.8x+28 \\ q(x)=-0.0021x^4-0.084x^3-0.0015x^3+2.94x^2-0.06x^2-0.02x^2+2.1x-0.8x+28 \\ q(x)=-0.0021x^4-0.0855x^3+2.86x^2+1.3x+28 \end{gathered}$

Therefore, the polynomial that can be used to model the total cost is;

$q(x)=-0.0021x^4-0.0855x^3+2.86x^2+1.3x+28$