Open Note Flashcard: Exponential Functions (growth/decay)

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 a quantity increases by a consistent percentage over equal time intervals, represented by a function of the form f(x) = a(b^x) where b > 1.

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 time intervals, represented by a function of the form f(x) = a(b^x) where 0 < b < 1.

Front

How can you identify an exponential function from a table of values?

Back

An exponential function will show a constant ratio between consecutive values, indicating that the output is multiplied by the same factor as the input increases.

Front

What is the general form of an exponential growth function?

Back

The general form is f(x) = a(b^x) where 'a' is the initial value and 'b' is the growth factor greater than 1.

Front

What is the general form of an exponential decay function?

Back

The general form is f(x) = a(b^x) where 'a' is the initial value and 'b' is the decay factor between 0 and 1.

Front

What is the significance of the base 'b' in an exponential function?

Back

The base 'b' determines the rate of growth or decay; if b > 1, the function represents growth, and if 0 < b < 1, it represents decay.

Front

How do you determine if a graph represents a linear or exponential function?

Back

A linear function produces a straight line, while an exponential function produces a curve that increases or decreases rapidly.

Front

What does the equation y = 40(1/2)^x represent?

Back

This equation represents an exponential decay function where the initial value is 40 and the quantity decreases by half for each unit increase in x.

Front

What does the equation y = 7(5/4)^x represent?

Back

This equation represents an exponential growth function where the initial value is 7 and the quantity increases by 25% for each unit increase in x.