According to modern​ science, Earth is about 4.5 billion years old and written human history extends back about​ 10,000 years. Suppose the entire history of Earth is represented with a 10001000​-meter-long ​timeline, with the birth of Earth on one end and today at the other end.
a. What distance represents 11 billion​ years?
b. How far from the end of the timeline does written human history​ begin?
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Part 1
a. 11 billion years is represented by enter your response here metersmeters of the timeline.
​(Type an integer or decimal rounded to the nearest tenth as​ needed.)

We are given that the entire history of Earth, 4.5 billion years, is represented on a timeline of 1000 meters. To solve these problems, we will use a proportional relationship between the years and the distance.

### Part a:
We need to determine the distance that represents 1 billion years on the timeline.

1. The ratio of distance to time is:
   \[
   \frac{1000 \, \text{meters}}{4.5 \, \text{billion years}}
   \]
   To find the distance that represents 1 billion years, we divide 1000 meters by 4.5:
   \[
   \text{Distance for 1 billion years} = \frac{1000}{4.5} \approx 222.2 \, \text{meters}
   \]

### Part b:
We now calculate the distance that represents 10,000 years of written human history.

1. First, we convert 10,000 years to billions of years by dividing by 1,000,000,000:
   \[
   10,000 \, \text{years} = \frac{10,000}{1,000,000,000} = 0.00001 \, \text{billion years}
   \]
   
2. Using the ratio of 1 billion years corresponding to 222.2 meters, we can find the distance:
   \[
   \text{Distance for 10,000 years} = 0.00001 \times 222.2 = 0.0022 \, \text{meters}
   \]

Thus, written human history begins approximately 0.0022 meters, or 2.2 millimeters, from the end of the timeline.

Would you like further details or have any other questions?

Here are five questions that extend from this topic:
1. How would you represent the formation of the solar system on this timeline?
2. What would the distance represent for the extinction of the dinosaurs, around 65 million years ago?
3. How does this timeline relate to the appearance of early humans?
4. What fraction of Earth's history does written human history represent?
5. If the timeline were extended to 2000 meters, how would the distances change?

**Tip:** Using proportional relationships can help solve many real-world math problems!

According to modern science, Earth is about 4.5 billion years old and written human history extends back about 10,000 years. Suppose the entire history of Earth is represented with a 1000-meter-long timeline, with the birth of Earth on one end and today at the other end. a. What distance represents 1 billion years? b. How far from the end of the timeline does written human history begin?

Explore how to use proportional reasoning to represent Earth's 4.5 billion-year history on a 1000-meter timeline. Learn how to calculate distances for 1 billion years and the start of written human history, using key mathematical concepts such as unit conversion and ratios. Suitable for students in Grades 6-8.

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