Understanding Exponential Functions Concepts

This lesson covers exponential functions, including their definition, graphing, and characteristics. It explains how to model real-world scenarios, such as virus spread, using exponential functions. The lesson also compares linear and exponential growth, providing examples and exercises to reinforce understanding.

What is the main focus of algebra lesson 62?

• Linear equations

• Exponential functions

• Logarithmic functions

• Quadratic functions

In an exponential function, what does the variable 'x' represent?

• The constant multiplier

• The y-intercept

• The exponent that changes

• The base of the function

How do you calculate 2 raised to the power of -2 using a calculator?

• 2 / 2

• 2 * -2

• 2 ^ -2

• 2 ^ 2

What is the value of 2 raised to the power of 0?

• 0

• 1

• 2

• Undefined

What happens to the graph of an exponential function when the base is greater than 1?

• It increases

• It decreases

• It remains constant

• It oscillates

What is the domain of an exponential function?

• All negative numbers

• All real numbers

• Only integers

• All positive numbers

What is an asymptote in the context of exponential functions?

• A line that the graph intersects

• A line that the graph approaches but never touches

• A point where the graph stops

• A point where the graph crosses the x-axis

In the example of the virus spreading, what does the function f(x) = 5^x represent?

• The total network size

• The rate of infection

• The number of computers infected

• The number of hours

How long does it take for the virus to infect 1000 computers?

• 3 hours

• 4.3 hours

• 5 hours

• 6 hours

What is the formula for an exponential function?

• f(x) = ax + b

• f(x) = a + b^x

• f(x) = a * b^x

• f(x) = a / b^x