Exponential Functions

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

Multiple Select

Which of the following are exponential functions?

• f(x)=4(2)^x

• y=4x²

• y=5^x

• f(x)=3x⁴

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 y-intercept of f(x)=5(3)^x

• (0,5)

• (0,3)

• (3,0)

• (5,0)

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)