Exponential Functions and Their Properties

The video tutorial explains how to determine the parameters of an exponential function, specifically the initial value 'a' and the common ratio 'r'. It starts by introducing the concept of exponential functions and provides specific values for h(n) at different n. The tutorial then demonstrates how to calculate the common ratio using these values and explores two methods to find the initial value. The first method uses a tabular approach, while the second method involves solving equations directly. Both methods are shown to yield the same result, illustrating the flexibility in solving exponential functions.

What is the general form of an exponential function?

• a * n^r

• a + n^r

• a + r^n

• a * r^n

If h(2) = 144 and h(4) = 324, what is the simplified ratio of h(4) to h(2)?

• 2/3

• 4/3

• 9/4

• 3/2

What is the value of r if r^2 = 9/4?

• 1/2

• 4/3

• 3/2

• 2/3

In the tabular method, what is the value of h(1) if h(2) = 144 and r = 3/2?

• 64

• 96

• 48

• 72

What is the initial value a if h(0) is calculated using the tabular method?

• 96

• 32

• 64

• 48

Using the direct calculation method, what is the value of a if h(2) = 144 and r = 3/2?

• 32

• 48

• 64

• 96

What is the value of a if a * (9/4) = 144?

• 64

• 96

• 48

• 32

Which method is described as easier for calculating the initial value a?

• Tabular Method

• Trial and Error Method

• Direct Calculation Method

• Graphical Method

What is the common ratio r in the exponential function h(n) = 64 * (3/2)^n?

• 2/3

• 3/2

• 4/3

• 1/2

What is the initial value a in the exponential function h(n) = 64 * (3/2)^n?

• 32

• 48

• 64

• 96