The scenario describes an exponential increase in the number of blossoms until the tree reaches maturity. An exponential increase is typically represented by a curve that starts slow and increases more rapidly over time. Therefore, we can eliminate the options that do not match this description.
1. **Option 1**: A line that increases from 0 to 3 years then decreases from 3 to 7 years.
- This does not match the description of an exponential increase.
2. **Option 2**: A curved line that increases from 0 to 8 years.
- This fits the description of an exponential increase, as it suggests a rapid increase over time until maturity.
3. **Option 3**: A straight line that increases from 0 to 9 years.
- A straight line suggests a constant rate of increase, not an exponential one.
4. **Option 4**: A curved line that decreases from 0 to 9 years.
- This represents a decrease, which does not fit the scenario of blossoming increasing exponentially.
Therefore, the correct graph that shows \( y \), the number of blossoms expected on a flowering tree, for each year after the young tree is planted, \( x \), would be:
- **Option 2**: A curved line that increases from 0 to 8 years.
If a flowering tree is cared for properly, the number of blossoms produced on the tree will exponentially increase until the tree reaches maturity. Which graph could show y, the number of blossoms expected on a flowering tree, for each year after the young tree is planted, x?
A graph shows age of trees (years) labeled 1 to 10 on the horizontal axis and number of blossoms on the vertical axis. A line increases from 0 to 3 years then decreases from 3 to 7 years.
A graph shows age of trees (years) labeled 1 to 10 on the horizontal axis and number of blossoms on the vertical axis. A curved line increases from 0 to 8 years.
A graph shows age of trees (years) labeled 1 to 10 on the horizontal axis and number of blossoms on the vertical axis. A straight line increases from 0 to 9 years.
A graph shows age of trees (years) labeled 1 to 10 on the horizontal axis and number of blossoms on the vertical axis. A curved line decreases from 0 to 9 years.
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