ACT Preparation / Unit 12 ACT 1106 worked example, 60 to 90 seconds
Telling Linear From Exponential in a Table
The idea
To classify a table, work in three steps. First, confirm the inputs are equally spaced; if not, compare changes per unit of input. Second, subtract consecutive outputs: equal differences mean linear, with the slope equal to the difference per step. Third, if the differences are not equal, divide consecutive outputs: equal ratios mean exponential, with the ratio as the growth factor per step. If neither holds, the function is neither.
In practice
Worked example: x = 0, 1, 2, 3 with outputs 80, 40, 20, 10. The differences, −40, −20, −10, are not equal. The ratios, 40/80, 20/40 and 10/20, all equal 0.5. The function is exponential, f(x) = 80(0.5)ˣ, halving each step. A second table, 5, 8, 11, 14, has differences of 3, so it is linear: y = 3x + 5.
Where people slip
Single source, the anchor only, as video 1105 says. A table can look linear for two steps and diverge later, so check every consecutive pair.
Your place on the trail
Every lesson rests on earlier ones and opens later ones. Tap any to jump.
Builds on
Unlocks
- Nothing yet depends on this.
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