Exponential Functions and Applications

The video tutorial explains exponential functions, which are functions of the form f(x) = B^x, where B is the base greater than zero and not equal to one, and x is any real number. The tutorial provides examples of exponential functions, such as f(x) = 2^x and f(x) = e^(x+1), and emphasizes the importance of using calculators for evaluation. Two practical examples are discussed: calculating average spending at a shopping mall and modeling the gray wolf population in the western Great Lakes. The key takeaway is that exponential functions have variables in the exponent.

What is the form of an exponential function?

• f(x) = B^x, where B > 0 and B ≠ 1

• f(x) = B^x, where B is any integer

• f(x) = B^x, where B < 0

• f(x) = B^x, where B = 1

Which of the following is NOT a valid base for an exponential function?

• 10

• 0

• e

• 2

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

• f(x) = x + 5

• f(x) = x^2

• f(x) = 3^x

• f(x) = 2x + 3

Why is a calculator often used to evaluate exponential functions?

• Because they are impossible to evaluate manually

• Because they are only defined in calculators

• Because they are difficult to evaluate manually

• Because they require complex algorithms

In the shopping mall example, what does the variable X represent?

• The number of stores visited

• The total amount spent

• The number of hours spent

• The number of items bought

What is the approximate amount spent after 4 hours in the shopping mall example?

• $350

• $300

• $250

• $200

In the gray wolf population example, what year is used as the starting point for X?

• 2018

• 1978

• 1980

• 1970

How many years after 1978 is the gray wolf population calculated for 2018?

• 45 years

• 40 years

• 35 years

• 30 years

What is the approximate gray wolf population in 2018 according to the model?

• 4198 wolves

• 5000 wolves

• 3000 wolves

• 4000 wolves

What is the key characteristic of an exponential function?

• The exponent is a variable

• The base is always 1

• The exponent is always 1

• The base is a variable