2.5.A.1Concept
Exponential functions model growth patterns where successive output values over equal-length input-value intervals are proportional. When the input values are whole numbers, exponential functions model situations of repeated multiplication of a constant to an initial value.
ExampleIs the table exponential?1 / 3
The table gives f at equally spaced inputs. Decide whether f is exponential. If so, write f(x) = abx and find f(4).
| x | 0 | 1 | 2 | 3 |
| f(x) | 12 | 18 | 27 | 40.5 |
Try it on paper first, then reveal each step to check your work.
Step 1 — Compare ratios
18 ÷ 12 = 1.5, 27 ÷ 18 = 1.5, 40.5 ÷ 27 = 1.5. The outputs are proportional over equal-length intervals.