Question

6.3.3 quiz: nonlinear models
the quadratic regression equation that models these data is ( y = -0.34x^{2}+4.43x + 3.46 ). using the quadratic regression equation, what was the predicted profit in year 8?
a. $17 million
b. $17.14 million
c. $16 million
d. $16.8 million

Explanation:

Step1: Substitute \(x = 8\) into the quadratic equation

Given the quadratic regression equation \(y=-0.34x^{2}+4.43x + 3.46\). Substitute \(x = 8\) into the equation.

$$y=-0.34\times8^{2}+4.43\times8+3.46$$

Step2: Calculate \(8^{2}\)

\(8^{2}=64\). Then the equation becomes \(y=-0.34\times64 + 4.43\times8+3.46\)

Step3: Calculate each product

\(-0.34\times64=-21.76\), \(4.43\times8 = 35.44\)

Step4: Calculate the sum

$$y=-21.76+35.44 + 3.46$$

$$y=( - 21.76+35.44)+3.46$$

$$y = 13.68+3.46$$

$$y=17.14$$

Answer:

B. \(17.14\) million