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 a positive real number, and 'x' is the exponent.

Front

What distinguishes exponential growth from exponential decay?

Back

Exponential growth occurs when the base 'b' in the function f(x) = a * b^x is greater than 1. Exponential decay occurs when 'b' is between 0 and 1.

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?

Back

An exponential function graph will show a rapid increase (growth) or decrease (decay) and will not form a straight line.

Front

What does the 'a' represent in the exponential function f(x) = a * b^x?

Back

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

Front

What does the 'b' represent in the exponential function f(x) = a * b^x?

Back

The 'b' represents the growth (b > 1) or decay (0 < b < 1) factor.

Front

If a function is modeled as A = 1200(0.85)^x, what type of function is it?

Back

It is an exponential decay function because the base (0.85) is less than 1.

Front

What is the y-intercept of the function A = 1200(0.85)^x?

Back

The y-intercept is 1200, which is the initial amount when x = 0.

Front

How do you determine if a graph represents exponential growth or decay?

Back

If the graph rises steeply as x increases, it represents exponential growth. If it falls steeply, it represents exponential decay.