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Cogito

Integrated Math 3 · Chapter 4 · Lesson 1

Practice Worksheet

Exponential Functions and Models

Growth that feeds on itself.

12 problems · about 21 minutes · F-LE.A.1, A-SSE.B.3

NameDate

Figure — use these to answer the problems

Set the factor above 1 for growth and below 1 for decay, then watch the two behave quite differently.
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y = 1 · 1.5^x + 0
a, initial amount1
b, growth factor1.5
Figure 1

Warm Up

Straightforward practice. Get the method working first.

5 problems

  1. A 15% 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 start.

  3. A 20% rise. Growth factor?

    Answer

  4. A 30% 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. $200 at 50% growth for 2 years. Final amount in dollars?

    Answer

  2. 160 g halves every hour. Grams after 4 hours?

    Answer

  3. A population doubles every 5 years. Factor over 15 years?

    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: Saving 50 dollars every week · A tank filling at 3 litres a minute · A balance growing 6 percent a year · A car losing 15 percent of its value each year

    Linear

    Exponential

  2. A 25% rise. Growth factor?

    Answer

  3. The Factor

    A 6% annual rise. What is the growth factor?

    Answer

  4. The Balance

    $500 at 10% compounded annually. Balance after 2 years, in dollars?

    Answerdollars