Exponential Growth or Decay?

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, leading to a rapid increase. For example, if a population doubles every year, it is experiencing exponential growth.

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. For example, if a radioactive substance loses half of its mass every year, it is experiencing exponential decay.

Tags

CCSS.HSF-IF.C.8B

Front

Identify the general form of an exponential growth equation.

Back

The general form is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

Identify the general form of an exponential decay equation.

Back

The general form is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

What does the base of an exponential function represent?

Back

The base of an exponential function indicates the growth or decay factor. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Tags

CCSS.HSF-IF.C.8B

Front

How can you determine if a table represents exponential growth or decay?

Back

If the values in the table increase by a consistent percentage, it represents exponential growth. If they decrease by a consistent percentage, it represents exponential decay.

Tags

CCSS.HSF-LE.A.1A

Front

What is the effect of a negative growth rate in an exponential function?

Back

A negative growth rate indicates exponential decay, meaning the quantity decreases over time.

Tags

CCSS.HSF-IF.C.8B

Front

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

Back

The initial value (a) represents the starting amount before any growth or decay occurs.

Tags

CCSS.HSF-IF.C.8B

Front

How does compounding affect exponential growth?

Back

Compounding increases the amount of growth in exponential functions, as the growth builds on itself over time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the difference between linear and exponential growth?

Back

Linear growth increases by a constant amount, while exponential growth increases by a constant percentage, leading to much larger values over time.