Exponential Functions: Intro

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What does it mean for a function to exhibit exponential growth?

Back

Exponential growth occurs when the growth rate of a function is proportional to its current value, leading to rapid increases over time.

Front

What does it mean for a function to exhibit exponential decay?

Back

Exponential decay occurs when the value of a function decreases at a rate proportional to its current value, leading to rapid decreases over time.

Front

How do you identify the y-intercept of an exponential function?

Back

The y-intercept of an exponential function f(x) = a * b^x is the value of 'a', which represents the initial value when x = 0.

Front

What is the y-intercept of the function f(x) = 2(4)^x?

Back

The y-intercept is 2.

Front

What is the y-intercept of the function f(x) = 13(0.27)^x?

Back

The y-intercept is 13.

Front

In the function y = 100 * 2^x, what does the '100' represent?

Back

The '100' represents the initial value or y-intercept of the function.

Front

What does the base of an exponential function indicate?

Back

The base indicates the growth or decay factor; if the base is greater than 1, the function exhibits growth, and if it is between 0 and 1, it exhibits decay.

Front

If a function has a base of 2, what type of growth does it represent?

Back

It represents exponential growth.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a * b^x, where 0 < b < 1.