Exploring Exponential Functions and Sequences

The video tutorial reviews exponential functions and sequences, covering initial values, growth and decay factors, and real-world applications. It includes examples of population growth, value depreciation, and sequence identification. The tutorial also guides on writing sequence formulas and solving exponential problems.

What does the variable 'a' represent in an exponential function?

• Time period

• Initial value

• Growth rate

• Decay factor

If the growth factor 'B' is less than 1, what type of exponential function is it?

• Growth

• Stable

• Decay

• Oscillation

What is the future population of deer after 4 years if it grows by 2% annually from an initial population of 1500?

• 1580

• 1623

• 1645

• 1600

How much will a boat worth 8350 decrease in value after 5 years if it depreciates by 12% annually?

• 4200

• 4800

• 5000

• 4406

What is the estimated population of crickets after 3 years if it doubles every month starting from 40?

• 275 thousand

• 2.75 trillion

• 2.75 billion

• 275 million

Using exponential regression, what is the approximate temperature of water after 6 intervals if it starts at 198.67 and decreases by 13% each interval?

• 90

• 86.15

• 100

• 95

What type of sequence is characterized by a constant ratio between consecutive terms?

• Quadratic

• Linear

• Geometric

• Arithmetic

What is the common difference in an arithmetic sequence where each term decreases by 0.5?

• -0.05

• 0.05

• 0.5

• -0.5

What is the initial value of a sequence where the first term is 3 and it follows an arithmetic progression?

• 5

• 3

• 0

• 1

In a geometric sequence, if the first term is 49 and the common ratio is 1/7, what is the formula for the nth term?

• 49 * (1/7)^(n-1)

• 49 + (1/7)^(n-1)

• 49 * (7)^(n-1)

• 49 + (7)^(n-1)