6.2 Exponential Functions

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 a positive real number, and 'x' is the exponent. It represents growth or decay processes.

Front

What does the initial value in an exponential function represent?

Back

The initial value in an exponential function, represented by 'a' in f(x) = a * b^x, is the value of the function when x = 0.

Front

What is the horizontal asymptote of an exponential function?

Back

The horizontal asymptote of all exponential functions is the x-axis, or y = 0.

Front

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

Back

To find the y-intercept of an exponential function, evaluate f(0). This gives the value of the function when x = 0.

Front

What is the common ratio in an exponential function?

Back

The common ratio in an exponential function is the factor by which the function's value changes as x increases by 1. It is represented by 'b' in f(x) = a * b^x.

Front

If f(x) = 0.05(2)^x, what is the initial value?

Back

The initial value is 0.05.

Front

If f(x) = 2 * 4^x, what is the y-intercept?

Back

The y-intercept is 2.

Front

What is the general form of an exponential growth function?

Back

The general form of an exponential growth function is f(x) = a * b^x, where b > 1.

Front

What is the general form of an exponential decay function?

Back

The general form of an exponential decay function is f(x) = a * b^x, where 0 < b < 1.

Front

How do you determine if a function is exponential?

Back

A function is exponential if it can be expressed in the form f(x) = a * b^x, where 'a' is a constant and 'b' is a positive real number.