https://file.aiquickdraw.com/mathbot/file/1727819605217q72vy0kt.jpg

The image shows a table representing the values of \( x \) (years after 1965) and \( y \) (profit in millions), along with a linear model \( Y = 1.19X + 13.68 \). The task is to estimate the profit in the year 1970 using this model.

To find the profit in 1970:
1. First, calculate \( X \) for 1970:
   \[
   X = 1970 - 1965 = 5
   \]
2. Substitute \( X = 5 \) into the equation \( Y = 1.19X + 13.68 \):
   \[
   Y = 1.19(5) + 13.68
   \]
   \[
   Y = 5.95 + 13.68
   \]
   \[
   Y = 19.63
   \]

Thus, the estimated profit in 1970 is **19.63 million**.

Would you like more details or have any questions about this process?

Here are 5 questions that expand on this:
1. How is the slope \(1.19\) in the linear equation interpreted in this context?
2. What would the estimated profit be for 1975 using the same model?
3. What does the y-intercept \(13.68\) represent in this scenario?
4. How can you determine whether the linear model is a good fit for the data?
5. What impact would a change in slope have on future profit estimates?

**Tip**: A linear model assumes that the relationship between variables remains constant over time, so be cautious when extrapolating far beyond the data range.

Use the model Y = 1.19X + 13.68 to estimate the profit in 1970.

Learn how to estimate the profit for a company in 1970 using the linear model Y = 1.19X + 13.68. This math problem explores key algebraic concepts and data modeling, ideal for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation