Let  
ˆ
y
  represent the profit (or loss) for a certain company  
x
  years after 1965. Based on the data shown below, a statistician calculates a linear model  
ˆ
y
=
1.93
x
+
18.32
 .

x
 	 
y
 
4	27.04
5	29.45
6	28.26
7	32.37
8	31.48
9	36.59
10	37.7
11	37.21
12	42.32
13	44.63
14	46.04
15	48.05
16	48.06
17	51.57


Use the model to estimate the profit in 1969. Round to the nearest cent.

The estimated profit in 1969 is

To find the estimated profit in 1969, we need to use the given linear model:

\[
\hat{y} = 1.93x + 18.32
\]

where $ x $ represents the number of years after 1965.

### Step 1: Determine $ x $ for the year 1969
Since 1969 is 4 years after 1965:
\[
x = 4
\]

### Step 2: Substitute $ x = 4 $ into the linear model
\[
\hat{y} = 1.93(4) + 18.32
\]

Calculating this:
\[
\hat{y} = 7.72 + 18.32 = 26.04
\]

### Conclusion
The estimated profit in 1969 is **$26.04**.

Would you like more details or have any questions?

---

Here are some related questions:
1. How would the profit estimate change if we used a quadratic model instead?
2. What would the profit estimate be in 1975 using the same model?
3. How does the profit change per year according to this model?
4. What does the slope of 1.93 represent in this context?
5. How would errors in actual data affect the accuracy of this model?

**Tip:** In linear models, the slope gives insight into the rate of change. Here, it shows how profit changes each year after 1965.

Let ŷ represent the profit (or loss) for a certain company x years after 1965. Based on the data shown below, a statistician calculates a linear model ŷ = 1.93x + 18.32. Use the model to estimate the profit in 1969. Round to the nearest cent.

Learn how to use the linear model ŷ = 1.93x + 18.32 to estimate profit for a company in 1969, based on years since 1965. This problem demonstrates essential algebra and linear modeling concepts, suitable for students in Grades 9-10.

Math Problem Statement

Let
ˆ y represent the profit (or loss) for a certain company
x years after 1965. Based on the data shown below, a statistician calculates a linear model
ˆ y

Solution

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