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, resulting in a rapid increase. For example, if a population grows by 10% each year, it will grow faster each subsequent year.

Tags

CCSS.HSF-LE.A.1A

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over time, leading to a rapid decrease. For example, if a substance loses 5% of its mass each year, it will lose more mass each subsequent year.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general formula for exponential growth?

Back

The general formula for exponential growth is y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time.

Tags

CCSS.HSF-IF.C.8B

Front

What is the general formula for exponential decay?

Back

The general formula for exponential decay is y = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is the time.

Tags

CCSS.HSF-IF.C.8B

Front

How do you identify exponential growth from a graph?

Back

Exponential growth graphs show a J-shaped curve that rises steeply as x increases, indicating that the quantity is increasing rapidly.

Tags

CCSS.HSF-IF.C.7E

Front

How do you identify exponential decay from a graph?

Back

Exponential decay graphs show a curve that decreases rapidly at first and then levels off, indicating that the quantity is decreasing over time.

Tags

CCSS.HSF-IF.C.7E

Front

What does a growth rate of 35% mean in an exponential function?

Back

A growth rate of 35% means that the quantity increases by 35% of its current value each time period.

Tags

CCSS.HSF-IF.C.8B

Front

If a function is represented as y = 15(1.35)^x, what does '15' represent?

Back

'15' represents the initial amount or starting value before any growth occurs.

Tags

CCSS.HSF.LE.B.5

Front

What is the difference between linear growth and exponential growth?

Back

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

Front

What is the significance of the base in an exponential function?

Back

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

Tags

CCSS.HSF-IF.C.8B