Question

According to modern science.earth is 4.5 billion yrs old and written human history extends about 10,000 yrs back. Suppose the entire history of earth is represented with a 10-meter-long timeline, with the birth of earth on one end and today on the other. What distance represents 1.5 billion years? How far from the end of the timeline does written history begin?

Answer 1

1.5 billion years = 3.33 meters

From the end 2.22\times 10^{-5} meters is the distance of written history.

Explanation:

Age of earth is 4.5 billion years and we have to represent the history of earth (from birth to present ) with a 10 meter long timeline.

So on the scale every meter will represent 4.5/10 = 0.45 billion years.

∵ 0.45 billion years represent the distance = 1 meter on scale.

∴ 1 billion years will be represented by =
`(1)/(.45) = (20)/(9) meters`

∴ For 1.5 billion years distance will be =
`(20)/(9)(1.5) = (30)/(9) = 3.33 meters`

Now we have to measure the length of written history from the end of the timeline.

Since written human history extends about 10000 yrs back means distance on timeline =
`((20)/(9))((10^(4) )/(10^(9)))` =
`2.22* 10^(-5) meters` from the end.