Table and Graph to Exponential Function

Front

What is an exponential function?

Back

Front

What does the base of an exponential function represent?

Back

The base of an exponential function determines the rate of growth or decay. If the base is greater than 1, the function represents exponential growth. If the base is between 0 and 1, it represents exponential decay.

Front

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

Back

To identify an exponential function from a table, check if the ratio of consecutive outputs (y-values) remains constant when the inputs (x-values) are increased by the same amount.

Front

What is the general form of an exponential equation?

Back

Front

How do you convert a table of values into an exponential equation?

Back

To convert a table of values into an exponential equation, identify the initial value (y-intercept) and the base by calculating the ratio of y-values for equal increments of x.

Front

What is the y-intercept in an exponential function?

Back

Front

What does it mean if an exponential function has a base of 1?

Back

Front

How do you determine the growth factor from an exponential equation?

Back

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base 'b' is greater than 1, leading to an increase in 'y' as 'x' increases. Exponential decay occurs when the base 'b' is between 0 and 1, leading to a decrease in 'y' as 'x' increases.

Front

How can you graph an exponential function?

Back

To graph an exponential function, plot the y-intercept, calculate additional points by substituting values for 'x', and draw a smooth curve that approaches the x-axis (for decay) or rises steeply (for growth).