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Cogito

Integrated Math 1 · Chapter 4 · Lesson 1

Practice Worksheet

Exponential Growth and Decay

Multiplying instead of adding.

12 problems · about 21 minutes · F-LE.A.1, F-LE.A.2

NameDate

Figure — use these to answer the problems

Set b above 1 for growth and below 1 for decay. Watch how differently the two curves behave.
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y = 1 · 1.5^x + 0
a, starting amount1
b, factor1.5
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. A 30% annual rise. What is the growth factor?

    Answer

  2. What distinguishes exponential from linear change?

    • It multiplies by a fixed factor rather than adding a fixed amount.
    • It is always faster from the very start.

  3. A 10% rise. Growth factor?

    Answer

  4. A 50% fall. Decay factor?

    Answer

  5. y = 100(2)ˣ at x = 3. What is y?

    Answer

Build It Up

The same ideas with more to keep track of.

3 problems

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

    Answer

  2. y = 200(1.5)ˣ at x = 2. What is y?

    Answer

  3. Does an exponential eventually overtake any linear growth? 1 yes, 0 no.

    Answer

Stretch Yourself

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

4 problems

  1. Sort each situation by the type of change.

    Write each item under the heading it belongs to: Adding 50 dollars a week · A tank filling at 3 litres a minute · A population growing 3 percent a year · A sample halving every hour

    Linear

    Exponential

  2. y = 50(3)ˣ at x = 2. What is y?

    Answer

  3. The Factor

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

    Answer

  4. The Decay

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

    Answer