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Cogito

AP Precalculus · Chapter 5 · Lesson 1

Practice Worksheet

Exponential Functions

Constant ratios instead of constant differences.

12 problems · about 21 minutes · AP Precalculus 2.1, 2.2, 2.3

NameDate

Figure — use these to answer the problems

Push the base above 1 for growth and below 1 for decay. Watch how differently each behaves.
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y = 1 · 2^x + 0
a, initial value1
b, growth factor2
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. 6, 12, 24, 48. Linear or exponential? 1 linear, 2 exponential.

    Answer

  2. What defines an exponential function?

    • Equal input intervals give a constant ratio of outputs.
    • The outputs grow quickly.

  3. 2, 6, 18, 54. Linear or exponential? 1 linear, 2 exponential.

    Answer

  4. 7, 12, 17, 22. Linear or exponential? 1 or 2?

    Answer

  5. f(x) = 100 · 2ˣ at x = 3. What is f?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

  1. f(x) = 80 · 0.5ˣ at x = 3. What is f?

    Answer

  2. A 40% annual fall. What is the decay factor?

    Answer

  3. f(x) = a · bˣ at x = 0. What is f, if a = 7?

    Answer

Stretch Yourself

Mixed problems. Work out what kind of question it is before you start.

4 problems

  1. Sort each pattern by the function type it indicates.

    Write each item under the heading it belongs to: Constant differences over equal intervals · A fixed amount added each step · Constant ratios over equal intervals · A fixed percentage change each step

    Linear

    Exponential

  2. 3, 9, 27, 81. What is the common ratio?

    Answer

  3. The Ratio

    5, 10, 20, 40. What is the common ratio?

    Answer

  4. The Factor

    A 25% annual rise. What is the growth factor?

    Answer