The video tutorial introduces exponential functions, highlighting their defining feature: the variable in the exponent. It explains the concept of initial value, which is the function's value when the input is zero, and the common ratio, which is the consistent factor between successive outputs. The tutorial also demonstrates how to construct exponential functions using these concepts.

What is the defining characteristic of an exponential function?

• The variable is in the base.

• The variable is in the numerator.

• The variable is in the denominator.

• The variable is in the exponent.

Which of the following is an example of an exponential function?

• h(n) = 1/4 * 2^n

• h(n) = 1/4 + 2^n

• h(n) = 1/4 / 2^n

• h(n) = 1/4 - 2^n

What is the initial value of the function h(n) = 1/4 * 2^n?

• 1

• 1/2

• 2

• 1/4

Tags

CCSS.HSF.LE.B.5

For the function f(t) = 5 * 3^t, what is the initial value?

• 5

• 3

• 1

• 15

What term is used to describe the number that the variable is raised to in an exponential function?

• Initial value

• Exponent

• Common ratio

• Base

Tags

CCSS.HSF.BF.A.2

What is the common ratio in the function h(n) = 1/4 * 2^n?

• 1/2

• 2

• 1/4

• 4

Tags

CCSS.HSF.BF.A.2

If h(0) = 1/4 and h(1) = 1/2, what is the common ratio?

• 2

• 1/2

• 4

• 1/4

Tags

CCSS.HSF.LE.A.2

Given the initial value of 5 and a common ratio of 6, what is the exponential function?

• G(x) = 5 + 6^x

• G(x) = 6 + 5^x

• G(x) = 6 * 5^x

• G(x) = 5 * 6^x

Tags

CCSS.HSF.LE.B.5

What is the initial value in the function G(x) = 5 * 6^x?

• 5

• 6

• 30

• 1

What is the common ratio in the function G(x) = 5 * 6^x?

• 6

• 30

• 1

• 5