Exponential function
SAT glossary · Math
Definition
A function of the form a·bx, with a constant ratio between successive equal steps. Distin- guished from linear (constant difference); confusing the two is the trap in growth items.
Exponential function in plain English
An exponential function has the form a · b^x, and what makes it 'exponential' rather than a straight line is HOW it grows: each time the input increases by exactly one step, the output gets multiplied by the same constant ratio b (rather than having the same constant amount added, which is what a linear function does). So a linear function grows by adding the same number over and over (like +5, +5, +5), while an exponential function grows by multiplying by the same number over and over (like × 1.05, × 1.05). Mixing these two up — treating steady percentage growth as if it were steady flat growth — is exactly the trap built into these questions.
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