Exponential Functions

Exponential Functions

Multiple Choice

What type of pattern do exponential functions have?

• Adds by the same number every time

• Multiplies by the same number every time

• Square roots all the inputs

• Squares all the inputs

Multiple Choice

What type of pattern do linear functions have?

• Adds by the same number every time

• Multiplies by the same number every time

• Square roots all the inputs

• Squares all the inputs

Multiple Choice

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

• SLOPE
• RATE OF CHANGE
• Y-INTERCEPT
• COMMON RATIO

Multiple Choice

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

• Slope

• Rate of change

• Y-intercept

• Multiplier

Multiple Choice

Identify the y-intercept (initial value) in the function f(x)=13(.27)^x

• (.27)^x
• .27
• 13
• 3.51

Multiple Choice

What is a, the starting term, for the function: f(x) = 300(1.16)^x?

• 300
• 1.16
• .16
• x

Multiple Choice

Identify the initial value:

y = 6.87 (4)^x

• a = 4

• a = 6.87

• a = 3

• a = 1

Multiple Choice

Which of the following is an increasing exponential function whose y-intercept is 50?

• y = 50(.05)^x
• y = 50x - 4
• y = (2)^x + 50
• y = 50(1.4)^x

If the ( ) are bigger than 1 it is growth. If the ( ) are smaller than 1 it is decay.

Multiple Choice

Is the pictured graph growth, decay, or linear or none?  

• Growth
• Decay
• Linear
• None

Multiple Choice

Is the pictured graph growth, decay, or linear or none?  

• Growth
• Decay
• Linear
• None

Multiple Choice

Is the following function and example of decay or growth?

f(x)=2(0.85)^x

• Exponential Decay

• Exponential Growth

Multiple Choice

The expression 12(1.015)^t models the population of elephants in a wildlife refuge after t years since 1975.
Is the population of elephants increasing or decreasing?

• Increasing
• Decreasing

Multiple Choice

Is the following function an example of decay or growth?

f(x) = 2(1.25)^x

• Exponential Growth

• Exponential Decay

Multiple Choice

Is this exponential growth or decay?

• Growth
• Decay

Finding the rate of growth or decay from an equation

• Is your 'b' bigger than 1? How much bigger? Times that # by 100 to get your %

• Is your 'b' smaller than 1? How much smaller? (1-b)? Times by 100 to find your %

Multiple Choice

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

• y = 15(35)^x
• y = 15(1.35)^x
• y = 15(0.35)^x
• y = 35(1.15)^x

Multiple Choice

The amount of ants in a colony, f, that is decaying can be modeled by                      f(x) = 800(.87)^x, where x is the number of days since the decay started. By what percentage is the colony decaying?

• 87%
• 13%
• 800%
• 8.7%

Writing an Exponential Function

• Your initial amount is always the starting #

• ( 1 plus or minus....

• divide the % by 100 to find the rate )

• exponent is always time

Multiple Choice

Write an equation that models the following situation:
Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

• y=6(0.14)^x
• y=6(1+14)^x
• y=6(1.14)^x
• y=6(0.86)^x

Multiple Choice

A new savings account is opened with $400 and gains 3% every year. What is the exponential function?

• f(x)=400(1+3)^x
• f(x)=400(1-0.03)^x
• f(x)=400(1+0.03)^x
• f(x)=400(0.03)^x