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Cogito

Algebra 1 · Chapter 6 · Lesson 1

Practice Worksheet

Exponential Growth and Decay

Multiplying by the same factor, over and over.

10 problems · about 20 minutes · F-LE.A.1, F-LE.A.2, F-IF.C.8

NameDate

Figure — use these to answer the problems

Set the base above 1 for growth and between 0 and 1 for decay.
-8-8-6-6-4-4-2-222446688
y = 1 · 2^x + 0
  • Point(2, 4)
Starting amount1
Factor per step2
Shift up0
Read at x2
Figure 1

Warm-Up Review

From earlier lessons. Loosen up before the new work.

2 problems

  1. From “Systems in Context”

    x + y = 12 and x − y = 2. What is x?

    Answer

  2. From “Solving Systems by Graphing”

    Slopes 3 and 3, intercepts 1 and 4. How many solutions?

    Answer

Warm Up

Straightforward practice. Get the method working first.

4 problems

  1. y = 4 · 2ˣ. What is y when x = 3?

    Answer

  2. What distinguishes exponential from linear growth?

    • A constant ratio between steps, not a constant difference.
    • It is faster.

  3. y = 2 · 3ˣ. What is y when x = 3?

    Answer

  4. y = 5 · 2ˣ. What is y when x = 0?

    Answer

Build It Up

The same ideas with more to keep track of.

2 problems

  1. A 20% fall each year. The decay factor as a percent?

    Answer

  2. Does an exponential add or multiply each step?

    • Multiplies.
    • Adds.

Stretch Yourself

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

2 problems

  1. Doubling

    y = 3 · 2ˣ. What is y when x = 4?

    Answer

  2. The Factor

    A quantity rises 6% each year. What is the growth factor, as a percent of the original?

    Answerpercent