Question

6 multiple choice 1 point using the function $y = -0.15x^3 + 2.38571x^2 - 12.56429x + 37.02$, what is the predicted value if $x = 7$? \bigcirc 15.42 \bigcirc 14.52 \bigcirc -15.42 \bigcirc -14.52

Explanation:

Step1: Substitute \( x = 7 \) into the function

We have the function \( y=-0.15x^{3}+2.38571x^{2}-12.56429x + 37.02 \). Substitute \( x = 7 \) into each term:

• For the \( x^{3} \) term: \( -0.15\times(7)^{3}=-0.15\times343=-51.45 \)
• For the \( x^{2} \) term: \( 2.38571\times(7)^{2}=2.38571\times49\approx116.90 \)
• For the \( x \) term: \( -12.56429\times7\approx - 87.95 \)
• The constant term: \( 37.02 \)

Step2: Sum the terms

\( y=-51.45 + 116.90-87.95 + 37.02 \)
First, \( -51.45+116.90 = 65.45 \)
Then, \( 65.45-87.95=-22.5 \)
Finally, \( -22.5 + 37.02 = 14.52 \)

Answer:

14.52 (corresponding to the option "14.52")