Writing and Interpreting Exponential Functions STAAR Review

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 an exponential function to exhibit growth?

Back

An exponential function exhibits growth when the base 'b' is greater than 1 (b > 1). This means that as 'x' increases, the value of the function increases rapidly.

Front

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

Back

An exponential function exhibits decay when the base 'b' is between 0 and 1 (0 < b < 1). This means that as 'x' increases, the value of the function decreases.

Front

In the function g(x) = 73(4/5)^x, what type of exponential function is it?

Back

It is an exponential decay function because the base 4/5 is less than 1.

Front

In the function h(x) = 12.3(4.9)^x, what type of exponential function is it?

Back

It is an exponential growth function because the base 4.9 is greater than 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

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

How can you determine if an exponential function is growing or decaying from its equation?

Back

You can determine if an exponential function is growing or decaying by examining the base 'b'. If b > 1, it is growing; if 0 < b < 1, it is decaying.

Front

What is the significance of the constant 'a' in an exponential function?

Back

The constant 'a' represents the initial value or the y-intercept of the function when x = 0.

Front

What is the y-intercept of the function f(x) = 5(2)^x?

Back

The y-intercept is 5, which occurs when x = 0, giving f(0) = 5(2)^0 = 5.