Exponential Functions Characteristics and Exponential Growth and Decay

• Growth

• Decay

Identify the following exponential functions characteristics, then graph the function:

• H.A: y = 4

  y-intercept: (0, 4.03)

  Behavior: as x approaches +infinity then the function exponentially grows, as x approaches -infinity then the function approaches the H.A. where y = 4

• H.A: y = 4

  y-intercept: (0, -4.03)

  Behavior: as x approaches +infinity then the function exponentially grows, as x approaches -infinity then the function approaches the H.A. where y = 4

• H.A: y = -4

  y-intercept: (0, 4.03)

  Behavior: as x approaches +infinity then the function exponentially grows, as x approaches -infinity then the function approaches the H.A. where y = -4

• H.A: y = 4

  y-intercept: (0, 4.03)

  Behavior: as x approaches +infinity then the function approaches the H.A. where y = 4, as x approaches -infinity then the function exponentially increases

If b > 1 in an exponential function, then the function represents:

• exponential growth

• exponential decay

is the following graph representing exponential growth or exponential decay?

• Exponential Growth

• Exponential Decay

• yes, the following function is an exponential function with the following characteristics:

  1. a = constant factor

  2. b > 0

  3. c is a constant

• yes, the following function is an exponential function with the following characteristics:

  1. a = constant factor

  2. b < 0

  3. c is a constant

• no, the following function is an exponential function with the following characteristics because b < 0

• no, the following function is an exponential function with the following characteristics because b > 0 and a = positive number

• 1. Horizontal Shift = 3 units right

  2. Vertical Compression by 1/4

  3. Vertical shift by 4 units upward

  4. b = 1/2 = exponential decay

• 1. Horizontal Shift = 3 units left

  2. Vertical Compression by 1/2

  3. Vertical shift by 4 units upward

  4. b = 1/4 = exponential decay

• 1. Horizontal Shift = 3 units right

  2. Vertical stretch by 1/4

  3. Vertical shift by 4 units upward

  4. b = 1/2 = exponential decay

• 1. Horizontal Shift = 3 units right

  2. Vertical Compression by 1/4

  3. Vertical shift by 4 units downward

  4. b = 1/2 = exponential growth

• exponential growth

• exponential decay

• a = initial value of the equation

  b = represents the growth and decay of the function

• a = represents the growth and decay of the function

  b = initial value of the equation

is the following graph representing exponential growth or exponential decay?

• Exponential Growth

• Exponential Decay

In an exponential function, what does the 'a' represent? 

• SLOPE

• RATE OF CHANGE

• Y-INTERCEPT

• COMMON RATIO