Exponential Growth and Decay Review

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 20% 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 population decreases by 10% each year, it will decline faster each subsequent year.

Tags

CCSS.HSF-LE.A.1A

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

In the equation y = 530(1 - 0.04)^x, what does 0.04 represent?

Back

In this equation, 0.04 represents the decay rate of 4% per year.

Tags

CCSS.HSF-IF.C.8B

Front

How do you determine the y-intercept in an exponential equation?

Back

The y-intercept in an exponential equation of the form y = a(b)^x is the value of 'a', which represents the initial amount when x = 0.

Tags

CCSS.HSF-IF.C.7E

Front

If a population of 1000 is decreasing by 5% each year, what will the population be after 3 years?

Back

The population after 3 years will be approximately 857.66, calculated using the formula: y = 1000(1 - 0.05)^3.

Tags

CCSS.HSF-LE.A.1C

Front

What does it mean if an equation has a base greater than 1?

Back

If an equation has a base greater than 1, it indicates exponential growth.

Tags

CCSS.HSF-IF.C.8B

Front

What does it mean if an equation has a base between 0 and 1?

Back

If an equation has a base between 0 and 1, it indicates exponential decay.

Tags

CCSS.HSF-IF.C.8B

Front

In the context of depreciation, what does a 10% annual depreciation mean?

Back

A 10% annual depreciation means that the value of an asset decreases by 10% of its current value each year.