To find the year when the store's sales reach $150,000, we need to set up the equation and solve for $x$.

1. The model for the sales in thousands of dollars is: $y = 30 + 7x$ where $x$ is the number of years since 2005.

2. Since we want the sales to be $150,000, or $y = 150$ (in thousands), we substitute this value into the equation: $150 = 30 + 7x$

3. Solve for $x$: $150 - 30 = 7x$ $120 = 7x$ $x = \frac{120}{7}$ $x \approx 17.14$

4. Rounding 17.14 to the nearest year gives $x = 17$.

5. Since $x$ represents the number of years since 2005, we add 17 to 2005: $2005 + 17 = 2022$

Answer: The store's sales will reach $150,000 in the year 2022.

Would you like further details or have any questions?

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Here are some related questions:

1. What would the store's sales be in 2010 according to this model?
2. How much does the store's sales increase each year?
3. If the sales growth rate changed to $10,000 per year, how would the model adjust?
4. What is the base sales value in 2005 according to the model?
5. How would you interpret the intercept of this linear model?

Tip: In linear models, the slope represents the rate of change while the intercept represents the starting value.