Growth or decay: reading an exponential before you calculate it

Every exponential question on the Digital SAT is built from the same skeleton. Once you can read the skeleton, most of these questions stop being calculations and become observations.

The skeleton

a is the starting amount. b is what happens in one step. If b > 1 the quantity grows; if 0 < b < 1 it decays. Nothing else in the equation can change that.

Reading b from the sentence

A question that says “decreases by 12% each year” has already told you b. It is 0.88, and you did not need to solve anything to know it. Students who write the equation first and read it second lose thirty seconds per question here.

Where inspection fails

One case does need algebra: when the interval in the question is not the interval in the exponent — “every 18 months” inside a model written per year. Then the exponent has to be rewritten before b means anything.

Four questions to practise

Practise this on four questions in a row before you time yourself. Speed is a by-product of reading, not the goal of it.