AP Precalculus · Unit 2: Exponential and Logarithmic Functions · Lesson 2.3

Guided Practice: Exponential Functions

🧭 Guided Practice
Pick an essential knowledge statement, then step through worked examples one move at a time.
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2.3.A.1Concept

The general form of an exponential function is f(x) = abx, with the initial value a, where a ≠ 0, and the base b, where b > 0 and b ≠ 1. When a > 0 and b > 1, the exponential function is said to demonstrate exponential growth. When a > 0 and 0 < b < 1, the exponential function is said to demonstrate exponential decay.

ExampleClassify four functions1 / 3

Decide whether each function is exponential growth, exponential decay, or not an exponential function in general form: (1) f(x) = 5(1.2)x, (2) g(x) = 40(0.9)x, (3) h(x) = 7·1x, (4) k(x) = 2(−3)x.

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Try it on paper first, then reveal each step to check your work.

Step 1 — f(x) = 5(1.2)^x
a = 5 > 0 and b = 1.2 > 1. This is exponential growth (blue curve).
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