## Extrapolation Definition Example Essay

In these questions, **math meets science**. You might be thinking, “Wait, but the ACT Science section doesn’t let you use your calculator!” This is true! And this means the ACT Science questions that require calculations will only require very simple math that you can do by hand or in your head.

Calculation questions require you to find a specific value based on the figures provided. However, the value will not be shown in the figure. Using the information you are given, you will need to predict what would happen past the edges of the graph or between values on a table. **In this article, I'm going to cover interpolations and extrapolations, along with tips and realistic ACT Science practice questions.**

## Interpolations

The word itself seems complicated, but it simply means calculations of numbers between known data points (which are provided in the visuals). Let’s check out this ACT Science practice question:

Start by trying to locate the relevant data (aka the data mentioned in the question, the average change in AGTB at 75 m from the nearest clearing) in this scatterplot:

After examining the scatterplot, I see there are points marked at 70 and 80 m from the center of the plot to the nearest clearing, but not at 75 m, this gap in data is what makes this an interpolation question! You have the data that surround the point, but you need to figure out what the point is.

What mathematical calculation could you do (using the data you do have) to find the approximate average change in AGTB at 75 m from the center of the plot to the nearest clearing? Perhaps, averaging the average change in AGTB for 70 m and 80 m from the center of the plot to the nearest clearing? At 70m from the center of the plot to the nearest clearing, the average change in AGTB is about -3.1. At 80m from the center of the plot to the nearest clearing, the average change in AGTB is -2.2.

Now, calculate using the average formula:

Sum of the values / (divided by) the number of values:

((-2.2) + (-3.1)) / 2

= -5.2 / 2

= -2.6

Then, compare it to the answer choices: so, the answer is G.

**ACT Science Tip #1:** even if you were a little off in your data grabbing (let’s say you said at 80m from the center of the plot to the nearest clearing, the average change in AGTB was -2.1), you see the answer choices are widespread enough that you will get the answer choice right by just picking the answer closest to the average you found in your calculations.

**ACT Science Tip #2:** There is an alternate method to solve these questions when the answer choices are widespread (as they are in the question above). You can simply draw a line connecting the dots in the scatterplot, and then, you approximate the point at 75 m from the center of the plot to the nearest clearing. See my example below:

Using this method, you can approximate the average change in AGTB at -2.8. This is closest to answer G, so that is the correct answer. Through this method, you find the answer a lot quicker.

However, as I said before, this will only work for widespread answers. If -2.9 had been an answer, this method would not have been very effective, as you may have chosen incorrectly. So only use this method if the answer choices are widespread. Otherwise, stick to the process that will always work to answer these questions:

- Find the relevant data (two data points equidistant from the point in question)
- Average the data together to find the approximate value for the midpoint.
- Find the closest (or hopefully matching) answer

This process gets a little trickier in extrapolations, in which we'll calculate data that is beyond the bounds of what we're given.

## Extrapolations

In order to show how extrapolation works, we are going to work through an ACT Science practice question:

Using this table to answer the question:

This extrapolation, like all extrapolations, requires identifying a pattern in the data and predicting the next step in that pattern (in whichever direction the question's data lies). These patterns will always be relatively simple, so the steps we take are also relatively simple:

- Steps for every extrapolation question
- Pinpoint what we're figuring out: is it a value more or less than what we are given?
- Identify the relationship between 2 consecutive data points in the table or graph (it doesn't matter which points we use, as long as they are consecutive)
- Find the relationship between the data in the question and the data in the table
- Apply the pattern in the table to the new data point

Let’s follow these steps to solve the ACT Science practice question above: We're figuring out the density that would match 67.54 g of solution in the graduated cylinder according to the table. The relationship between 60.63 g of solution (the second to last entry in the table) and 64.64 g (the last entry in the table) is +4.01 g of mass and +0.08 g/ml of density.

The 67.54 g of solution (from the question) is above the highest step 64.64 g in the table. Figure out the exact mass difference between the two:

2.9 g is the mass difference as opposed to 4.01 g between the last and second to last entry. Between the second to last entry and last entry there was a +0.08 g/ml change in density. Since there is a slightly smaller mass change (about ¾ the amount of change between the last and second to last entry), the density change will be slightly smaller (about ¾ the amount of change between the last and second to last entry). So, the change should be about +0.06 g/ml. Add that to the last density value in the table (1.29).

So, the answer is H. Again, even if you were slightly off, you would have been closest to that answer choice.

If you feel unsure of this process, you're about to get some more practice in extrapolating information. Check out this ACT Science practice question:

Again, we follow the same steps: We need to use the table above. The highest given capacitance is 1.2 x 10^-6, and we are asked about 1.5 x 10^-6. The time for 1.2x 10^-6 was 8.3 seconds. The second highest given capacitance was 0.6 x 10^-6, and the time for it was 4.2 seconds. The difference in time between 1.2 and 0.6 (the second highest given capacitance) is 8.3 - 4.2 seconds. So the difference is +4.1 seconds.

## Recap

I hope you feel like a calculating machine! For every interpolation question,

- Find the relevant data (two data points equidistant from the point in question).
- Average the data together to find the approximate value for the midpoint.
- Find the closest (or hopefully matching) answer.

For every extrapolation question,

- Pinpoint what we're figuring out, is it a value more or less than what we are given?
- Identify the relationship between 2 consecutive data points in the table or graph. How much does the y-value increase or decrease as the x-value increases?
- Find the relationship between the data in the question and the data in the table. For example, is the data in the question 5 more or less than the data in the table?
- Apply the pattern in the table to the new data point.
- Find the closest (or hopefully matching) answer.

## What’s Next?

Now that you're a calculating machine learn about the other types of questions on the ACT Science section such as factual questions, interpreting trends questions, experimental design questions, and interpreting experiments questions.

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## Writing a Short Story Using Extrapolation

## Introduction

Scientific breakthroughs seem to be a daily occurrence. Many of these breakthroughs are connected to biotechnology. With the information gained from the Human Genome Project, there are certainly many more breakthroughs in our future. One of the techniques science fiction writers use is extrapolation, or using what is currently possible to speculate what future outcomes may be. By having students extrapolate an idea individually, they may think deeper about the possibilities for biotechnology. This activity asks them to extrapolate something that is currently possible (or at least almost) in biotechnology and write a story about what it might lead to in the future. The teacher may want to review the basic elements of a short story with the students prior to having them write their own stories.

## Objectives

The students will:

- demonstrate their understanding of the word extrapolation;
- create their own short story.

## Procedure

- Review the examples of extrapolation from the short story "Revenants" by Judith Tarr.
^{1} - Brainstorm with the class possible uses of biotechnology. Some examples:
- prolongation of life
- food production
- "perfect" babies
- detection of genetic problems
- cure of genetic problems
- combining human and animal genes
- restoring extinct animals
- eliminating skin color differences
- Students choose one of these uses upon which to base their short story. The story should take one of the possibilities of biotechnology and extrapolate what may be possible in the year 2025. Mention to students that although many science fiction writers tend to focus on negative results in their speculation of the future, the students are free to focus on the positive results in their own.
- Teachers should set their own parameters for length of the short story and for the inclusion of basic short story elements, such as plot, character, theme, setting, and point of view.
- Set a due date for the first drafts of the short stories.
- Students peer edit and receive feedback in read-around groups.
- Using this information, students revise their short stories.
- Set a due date for the final draft.

## Extensions

If time and resources permit, students can word-process their stories, illustrate them, and publish a class anthology of their short stories.

1. Tarr, Judith, "Revenants," in *Dinosaur Fantastic* edited by Mike Resnick and Martin H. Greenberg, (Daw Books, Inc.: 1993), pp. 67-77.

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