Exploring Exponential Functions

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Exploring Exponential Functions
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Exponential Function

• The independent variable (x) is an exponent.
• f(x) a bx
• a cannot be zero, b cannot be one and must be
  positive.

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Exponential Functions

• a is the initial amount or the amount with
  which you start.
• b is the growth or decay factor
• x is the number of times it grows or decays.

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Example 1

• Suppose that two mice live in a farmhouse. If
  the number of mice quadruples every 3 months, how
  many mice will be in the house after 2 years?
• Make a table.

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Example 1

• How many mice at the beginning (initial amount)?
• How many mice after 3 months?
• How many mice after 6 months?
• How many mice after 9 months?

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Example 1

• Replace a with the initial amount (2 mice).
• Replace b with what is happening to the number
  of mice (Being multiplied by 4).
• Replace x with the number of 4 month periods
  (8).

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Write an exponential function for

• There are 200 cells in a jar. The number of
  cells triples every hour.
• y 200 3x
• There are 5 cats on an island. The number of
  cats doubles every three weeks.
• y 5 2x
• There is 800 in a savings account. The amount
  doubles every 8 years.
• y 800 2x

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Evaluate each exponential function

• y 3x for x 1, 2, and 4
• y 2.5x for x 2, 3 and 4

• 3, 9, 81
• 6.25, 15.625, 39.0625
• (0.4, 0.16, 0.01024

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Graph y 5(2)x
Plug it into y. Go to the table. Pick points
that will fit on the grid.




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Graph y 3(1/2)x