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.

Front

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

Back

Exponential growth occurs when a quantity increases by a consistent percentage over equal intervals of time, resulting in a rapid increase.

Front

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

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over equal intervals of time, resulting in a rapid decrease.

Front

What is the initial value in an exponential function?

Back

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

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

Back

To find the y-intercept, evaluate the function at x = 0. For f(x) = a * b^x, the y-intercept is (0, a).

Front

What is the base in an exponential function?

Back

The base is the constant 'b' in the function f(x) = a * b^x, which determines the rate of growth or decay.

Front

What is the difference between linear and exponential functions?

Back

Linear functions have a constant rate of change, while exponential functions have a variable rate of change that increases or decreases exponentially.

Front

What is the general form of an exponential growth function?

Back

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

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.

Front

How can you identify an exponential function from a graph?

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An exponential function graph will show a curve that rises or falls rapidly, unlike a straight line for linear functions.