Questions: Complete parts a. to d b. Predict when the profit will be 12 million. The profit will be 12 million in the year 2007 c. What is the p-intercept of the model? What does it mean in this situation? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. (Type an ordered pair.) A. The p-intercept of the model is The p-intercept estimates the profit (in millions of dollars) of a company for the year 2000. B. The p-intercept of the model is . The p-intercept estimates the year for which the company has no profit.

Solution Steps

To solve the given problem, we need to model the relationship between time (years) and profit (millions of dollars) using the provided data. We can use linear regression to find a linear equation that fits the data. Once we have the equation, we can use it to predict when the profit will be $12 million and determine the p-intercept of the model.

1. Linear Regression: Use the given data points to perform linear regression and find the best-fit line equation in the form \( P = mt + c \), where \( P \) is the profit and \( t \) is the time in years.
2. Predict Profit: Use the linear equation to solve for \( t \) when \( P = 12 \) million.
3. Find p-intercept: The p-intercept is the value of \( P \) when \( t = 0 \). This will help us understand the initial profit estimation.

Using the provided data points, we performed linear regression to find the relationship between years \( t \) and profit \( P \). The resulting linear equation is given by:

\[ P = -4t + 40 \]

To find when the profit will be \$12 million, we set \( P = 12 \) and solve for \( t \):

\[ 12 = -4t + 40 \]

Rearranging gives:

\[ 4t = 40 - 12 \] \[ 4t = 28 \] \[ t = 7 \]

Thus, the profit will be \$12 million in the year \( 2000 + 7 = 2007 \).

The p-intercept occurs when \( t = 0 \). From our linear equation, we find:

\[ P = 40 \]

This means that the p-intercept is \( (0, 40) \), indicating that the estimated profit for the year 2000 is \$40 million.

Final Answer