Unitary Method
The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products.
Speed, Time, and Distance
Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.
Profit and Loss
The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.
Units and Measurements
Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.
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![### Exploring Growth Patterns
#### The Median Height of Girls Over Time
The function \( f(x) = 3.1 \sqrt{x} + 19 \) models the median height, \( f(x) \), in inches, of girls who are \( x \) months of age. The corresponding graph is displayed below:
#### Graph Analysis
![Graph of Girls' Heights]
- **Y-axis (Vertical):** Median Height (inches)
- **X-axis (Horizontal):** Age (months)
The plotted curve represents the function \( f(x) = 3.1 \sqrt{x} + 19 \).
#### Source:
Laura Walther Nathanson, *The Portable Pediatrician for Parents.*
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### Key Concepts
**a. Graph Transformations:**
- Describe how the given graph can be obtained using transformations of the square root function \( f(x) = \sqrt{x} \).
**b. Model Prediction:**
- Calculate the median height of girls who are 48 months (4 years) old using the model, rounding to the nearest tenth of an inch.
- Compare this predicted height with the actual median height at 48 months, which is 40.2 inches.
**c. Average Rate of Change (Birth to 10 Months):**
- Determine the average rate of change in inches per month between birth and 10 months using the model.
- Round to the nearest tenth.
**d. Average Rate of Change (50 to 60 Months):**
- Calculate the average rate of change in inches per month between 50 and 60 months using the model.
- Compare this result with the average rate of change found in part c and explain the differences using the graph.
By understanding these key concepts, we can gain valuable insights into the growth patterns of young girls and how their median height changes over time.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe97b18e0-da2d-4d6d-a0ca-770e5741a160%2Ff10501ec-34a5-422b-b5ac-d6a569edbd43%2F5ijx4ny.jpeg&w=3840&q=75)
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