The equation 

y equals 7.29 t plus 229.2y=7.29t+229.2 

represents the change in the college faculty salaries index for a particular​ college, where 2003 is the base​ year, year 0 and t is the number of years since 2003. Use the equation to predict when the index for faculty salaries will be 300.




To predict when the index for faculty salaries will be 300, we need to solve the equation:

\[
y = 7.29t + 229.2
\]

for the value of \( t \) when \( y = 300 \).

### Step 1: Substitute \( y = 300 \) into the equation.

\[
300 = 7.29t + 229.2
\]

### Step 2: Solve for \( t \).

First, subtract 229.2 from both sides to isolate the term with \( t \):

\[
300 - 229.2 = 7.29t
\]

\[
70.8 = 7.29t
\]

Next, divide both sides by 7.29 to solve for \( t \):

\[
t = \frac{70.8}{7.29} \approx 9.71
\]

### Step 3: Interpret the result.

The index for faculty salaries will be 300 approximately 9.71 years after 2003.

### Final Answer:

This corresponds to the year \( 2003 + 9.71 \approx 2012.71 \). So, sometime around late 2012 or early 2013, the index for faculty salaries is predicted to reach 300.

Would you like more details or have any further questions? Here are five related questions that could expand your understanding:

1. How would the result change if the starting index in 2003 was different?
2. What is the significance of the slope \( 7.29 \) in this context?
3. If you wanted to find the index in a specific year, how would you adjust the equation?
4. What does the y-intercept \( 229.2 \) represent in this scenario?
5. How could you adjust the equation to account for inflation or other economic factors?

**Tip:** When solving for \( t \), it's essential to remember that \( t \) represents the number of years since the base year, so the final prediction should always be interpreted in terms of actual calendar years.

Explore how to predict the growth of a college faculty salaries index using a linear equation model. Learn step-by-step how to solve for when the index reaches 300, based on the equation y = 7.29t + 229.2. Suitable for students in Grades 7-9.

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