Predicting new trials on ACT Science: extending an established pattern to an untested condition, using interpolation within the data and extrapolation beyond it, and stating the prediction's certainty.

What this topic is asking

A common Research Summaries question asks you to predict the outcome of a trial that was never run: the result at a temperature between two tested ones, or beyond the highest tested, or for a condition the experimenters did not include. The method is to find the pattern in the data and extend it to the new condition, while being honest about how certain the prediction is.

Step one: establish the pattern

Before predicting, describe the pattern the data already show:

• Direction: as the independent variable increases, does the result rise, fall, or stay flat?
• Rate or step: by how much does the result change per unit change in the variable (for a linear pattern), or is the change speeding up or slowing down?
• Turning points: does the trend peak and reverse, or plateau?

This is the same trend-reading skill as on a graph or table (reading line graphs and trends), now applied to forecast a missing value.

Step two: extend to the new condition

How you extend depends on where the new condition sits.

• Between tested values (interpolation): estimate proportionally. If the result is 4 at one tested value and 8 at the next, a condition halfway between is about 6.
• Beyond the tested values (extrapolation): continue the pattern past the last data point. For a steady linear rise, keep adding the same step.

The interpolation and extrapolation mechanics are developed in interpolation and extrapolation; here the point is to apply them to a predicted trial.

Step three: state the certainty

The ACT often asks not just for a predicted value but for a judgement about it. Two principles:

• A prediction within the tested range (interpolation) is reliable, because the data bracket it.
• A prediction beyond the tested range (extrapolation) is less certain, because the trend may level off, reverse, or change shape outside the data.

So a careful answer might be "the rate would likely be lower, because the trend was already falling," which states both the direction and the basis without overclaiming precision.

Predicting from a comparison

Predictions sometimes draw on a comparison between experiments rather than a single trend. If adding a catalyst doubled the rate at every tested temperature, you can predict that a new temperature would also show roughly double the rate with the catalyst, because the comparison held across the range. This combines the comparison logic of comparing experiments and results with extension.

Try this

Q1. A measurement is 10 at x = 5, 20 at x = 10, and 30 at x = 15, rising steadily. Predict the value at x = 20 and say whether this is interpolation or extrapolation. [2 points]

• Cue. Continuing the step of 10 per 5 units gives $30 + 10 = 40$ at x = 20; this is extrapolation, because 20 is beyond the tested range.

Q2. A rate peaked at a certain temperature and then fell. Why would extending the original rising line overestimate the rate at a much higher temperature? [2 points]

• Cue. Because the trend has reversed past the peak; the rate is now falling, so the prediction must follow the falling trend rather than the earlier rising line.