Exponential Functions Practice

Exponential Functions

Unit 5 Lesson 1

Exponential Functions have a variable in the exponent

Multiple Choice

Which of the following is an exponential function?

• y = x²

• f(x) = 3x³

• y = x³

• f(x) = 3^x

Exponential Functions

f(x) = a (b)^x

^{a = initial value or starting amount}

^{b= (common ratio) growth or decay factor}

Multiple Choice

What is the initial value in y=4(2)^x

• 4

• 2

• x

Multiple Choice

What is the y-intercept in y=4(2)^x

• (4,0)

• (0,2)

• x

• (0,4)

• (4,2)

Multiple Choice

What is the starting amount in the problem below?

f(t) = 300(1.05)^t

• 300

• 1.05

• t

• y

Multiple Choice

What is the growth rate in the problem below?

f(t) = 300(1.05)^t

• 300

• 1.05

• t

• y

Multiple Choice

What is the common ratio for the function f(x) = 25 (4)^x

• 25

• 4

Exponential

Growth vs. Decay

If b > 1 then Growth

If b is a fraction

0

Both Graphs have a

Horizontal Asymptote

(graph never touches

the X-axis)

b^x cannot equal 0

Multiple Choice

b⁰ =

• -1

• 0

• 1

Multiple Choice

The y-intercept for any function in the form

y=b^x

• (0,0)

• (0,1)

• (1,0)

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

Identify the initial value:

y = 6.87 (4)^x

• a = 4

• a = 6.87

• a = 3

• a = 1

Multiple Choice

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

• Growth

• Decay

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

Which function will show exponential behavior?

f(x) = (4.3)^x 

or

g(x) = 4.3x + 9

• f(x)

• g(x)

• both

• neither

Multiple Choice

Pick the equation that is exponential decay

• y = 2000(0.88)^x

• y = 0.5(1.88)^x

• y = 10(3/2)^x

• y = 0.8(13)^x

Multiple Choice

Classify the model as Exponential GROWTH or DECAY.
A=10(1.01)³

• Growth

• Decay

Multiple Choice

Suppose a culture of bacteria begins with 5000 cells and dies by 30% each year. Write an equation that represents this situation.

• y=5000(0.7)^x

• y=30(5000)^x

• y=5000(1.3)^x

• y=5000x^x

Multiple Choice

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

• Slope

• Rate of change

• Y-intercept

• Multiplier

Multiple Choice

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

• Slope

• Rate of change

• Y-intercept

• Multiplier

Multiple Choice

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

• Exponential Growth

• Exponential Decay

• Linear

• None

Multiple Choice

Is this exponential growth or decay?

• Growth

• Decay