Exponential Growth vs Decay

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase that can be represented by the function f(x) = a(1 + r)^x, where 'a' is the initial amount and 'r' is the growth rate.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease that can be represented by the function f(x) = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.

Tags

CCSS.HSF-IF.C.8B

Front

How can you identify exponential growth on a graph?

Back

Exponential growth is identified on a graph as a curve that rises steeply to the right, indicating that the quantity increases rapidly as the independent variable increases.

Tags

CCSS.HSF-IF.C.7E

Front

How can you identify exponential decay on a graph?

Back

Exponential decay is identified on a graph as a curve that falls steeply to the right, indicating that the quantity decreases rapidly as the independent variable increases.

Tags

CCSS.HSF-IF.C.7E

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 (b > 0), and 'x' is the exponent.

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, resulting in a straight line, while exponential functions increase or decrease by a constant percentage, resulting in a curve.

Front

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

Back

In an exponential function f(x) = a * b^x, the base 'b' represents the growth (b > 1) or decay (0 < b < 1) factor of the function.

Tags

CCSS.HSF-IF.C.8B

Front

What is an example of an exponential growth function?

Back

An example of an exponential growth function is f(x) = 2 * 3^x, where the quantity triples for each unit increase in 'x'.

Tags

CCSS.HSF-LE.A.1A

Front

What is an example of an exponential decay function?

Back

An example of an exponential decay function is f(x) = 5 * (0.5)^x, where the quantity halves for each unit increase in 'x'.

Tags

CCSS.HSF-LE.A.1A

Front

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

Back

The initial value 'a' in an exponential function represents the starting amount or value of the quantity at x = 0.

Tags

CCSS.HSF.LE.B.5