Exponential Equations from Tables & Graphs

Front

What is an exponential equation?

Back

Front

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

Back

An exponential function can be identified if the ratio of consecutive outputs (y-values) is constant when the inputs (x-values) are increased by equal intervals.

Front

What is the general form of an exponential equation?

Back

Front

What does the base of an exponential function represent?

Back

The base of an exponential function indicates 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 can you convert a table of values into an exponential equation?

Back

Front

What is the significance of the y-intercept in an exponential function?

Back

Front

How do you determine if a function is exponential from a graph?

Back

A function is exponential if its graph shows a rapid increase or decrease, forming a curve that either rises steeply (growth) or falls sharply (decay) as x increases.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when the base of the exponential function is greater than 1, leading to an increase in value over time. Exponential decay occurs when the base is between 0 and 1, resulting in a decrease in value over time.

Front

How do you write an exponential equation from a graph?

Back

Front

What is the role of the constant 'a' in an exponential equation?

Back