Question

8.3.3 quiz: nonlinear models
this table shows the profit for a company (in millions of dollars) in different
years.

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 10?
a. $13.76 million

Explanation:

Step1: Substitute \(x = 10\) into the quadratic equation

We are given the quadratic regression equation \(y=-0.34x^{2}+4.43x + 3.46\). Substitute \(x = 10\) into the equation.

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

First, calculate \(x^{2}\) when \(x = 10\). So, \(x^{2}=10^{2}=100\).

Step3: Calculate \(-0.34x^{2}\)

Substitute \(x^{2}=100\) into \(-0.34x^{2}\). We get \(-0.34\times100=-34\).

Step4: Calculate \(4.43x\)

Substitute \(x = 10\) into \(4.43x\). We have \(4.43\times10 = 44.3\).

Step5: Calculate the value of \(y\)

Now, substitute the values into the equation \(y=-0.34x^{2}+4.43x + 3.46\).
\(y=-34 + 44.3+3.46\)
\(y=10.3 + 3.46\)
\(y = 13.76\)

Answer:

A. \(13.76\) million