Writing Exponential Functions

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a(b^x), where 'a' is a constant, 'b' is the base (a positive real number), and 'x' is the exponent.

Front

What does the base 'b' in an exponential function represent?

Back

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

Front

How do you identify the common ratio in a sequence?

Back

The common ratio is found by dividing any term in the sequence by the previous term.

Front

What is the x-intercept of an exponential function?

Back

An exponential function does not have an x-intercept; it never crosses the x-axis.

Front

What is the general form of an exponential growth function?

Back

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

Front

What is the general form of an exponential decay function?

Back

The general form is y = a(b^x), where 'a' is the initial value and 0 < b < 1.

Front

How can you determine if a function is exponential from a table of values?

Back

If the ratio of consecutive outputs (y-values) is constant, the function is exponential.

Front

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

Back

The initial value 'a' represents the starting amount or value of the function when x = 0.

Front

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

Back

Exponential decay means that the value of the function decreases rapidly at first and then levels off, approaching zero but never reaching it.

Front

How do you write an exponential function from a word problem?

Back

Identify the initial value and the growth/decay factor, then use the form y = a(b^x) to write the function.