To determine which result presents a higher number of photos taken per week, we compare the rate of photos per week given in the study with the data collected from Vanessa's phone.

Step 1: The Study

The study states the following equation:

$y = 18x$

Here, $x$ is the number of weeks since the phone purchase, and $y$ is the total number of photos taken.
The rate of photos per week is 18 photos per week since the slope of $y = 18x$ is 18.

Step 2: Vanessa's Data

We calculate the photos per week based on the table provided.

From the table, Vanessa's data shows that the rate of photos per week is 19 photos per week.

Step 3: Compare the Results

• The study: 18 photos per week
• Vanessa's test: 19 photos per week

Conclusion:
Vanessa's results show a higher rate of photos taken per week than the study.

Would you like me to further explain how the rates were calculated or break down any part of the solution?

Here are some related questions for practice:

1. If the rate in the study was 20 photos per week, what would the equation become?
2. How many total photos would Vanessa have at 10 weeks if she continues taking 19 photos per week?
3. Can we model Vanessa's data using a linear equation? What would the equation look like?
4. How does changing the slope affect the total number of photos over time?
5. What is the difference in total photos between the study's model and Vanessa's data at 7 weeks?

Tip: When interpreting linear models, the slope tells you the rate of change — always check this for comparison!