Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the increase of a quantity is proportional to its current value, leading to growth at an increasing rate over time.

Front

What is exponential decay?

Back

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time.

Front

What is a linear function?

Back

A linear function is a function that creates a straight line when graphed, characterized by a constant rate of change.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is f(x) = a(b^x), where 'a' is a constant, 'b' is the base, and 'x' is the exponent.

Front

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

Back

The base 'b' in an exponential function represents the growth (b > 1) or decay (0 < b < 1) factor.

Front

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

Back

An exponential function can be identified by a constant ratio between consecutive outputs (y-values) for equal intervals of inputs (x-values).

Front

What is the difference between linear and exponential growth?

Back

Linear growth adds a constant amount over equal intervals, while exponential growth increases by a percentage of the current value, leading to faster growth over time.

Front

What is the common ratio in an exponential function?

Back

The common ratio is the factor by which the function's value multiplies for each unit increase in the independent variable.

Front

How can you graph an exponential function?

Back

To graph an exponential function, plot points for various values of x and connect them to show the curve that rises or falls steeply.

Front

What is the y-intercept of an exponential function?

Back

The y-intercept of an exponential function is the value of the function when x = 0, which is equal to 'a' in the function f(x) = a(b^x).