Question

You are going on an expedition to dig for dinosaur fossils. In digging you come across a small trunk left by another archeologist. In the trunk is a paper that lists how deep you need to dig to reach dinosaur fossils. Unfortunately, something spilled on part of the paper and it is damaged.

Using your knowledge of mathematics, find the missing numbers in the
chart. Write a generalization or rule to determine any number of feet you
must dig given the number of years.

If the Jurassic period was 200 million years ago, how deep would you need
to dig at this location to uncover fossils of that era? Explain why your
answer is or is not reasonable.

Answer 1

200,000 feet to dig

Explanation:

We use a ratio for this problem

30,000 200,000,000

----------- = ---------------------

30 x

200,000,000 * 30

---------------------------- = 200,000 feet to dig

30,000

This answer is reasonable because 200,000,000 years ago was a long time ago so then the person must dig a reasonable amount of dirt. So then 200,000 feet is reasonable.

Answer 2

The fossils of any historical era are found deep inside the earth. Their depth can be estimated by calculating based on the time they existed, for example - in years ago. Given that the current era's fossils are right at the surface, we make an assumption - any era was pushed 1 foot deep for every million years ago.

Now, let's calculate for the Jurassic period, which was 200 million years ago.

Step 1: Identify the number of years since the Jurassic period. In this case, we know that the Jurassic period was approximately 200 million years ago.

Step 2: Understand the rule for digging. In this case, we're assuming a rule of digging 1 foot for every 1 million years. This means that for every million years that have passed since the era in question, we would have to dig 1 foot deep to get to the level where we would find the fossils of that era.

Step 3: Use the rule to calculate the required depth. According to our rule, the depth required to dig would be equal to the number of years since the era, divided by the factor of the rule. In this case, the factor of the rule is 1 million years per foot.

So, we would divide the number of years since the Jurassic period (200 million) by the factor (1 million), which gives us 200. Therefore, we would need to dig 200 feet deep.

Therefore, based on the assumed ratio of 1 foot per 1 million years, the depth required to dig to uncover fossils of the Jurassic era is 200 feet.

This answer is reasonable because it is based on a clear and simple rule: the more time has passed since the era in question, the deeper we would need to dig to find its fossils. Of course, many other factors could affect the actual depth at which fossils are found, such as geological movements and erosion, but this gives us a good starting point.