Exponential Decay

Front

What is Exponential Decay?

Back

Exponential Decay is a process where a quantity decreases at a rate proportional to its current value, often represented by the equation f(x) = a(1 - r)^x, where 'a' is the initial amount, 'r' is the decay rate, and 'x' is time.

Tags

CCSS.HSF-IF.C.8B

Front

What does the equation f(x) = 2,000(0.97)^x represent?

Back

This equation represents the value of an aquarium that depreciates by 3% per month, starting at $2,000.

Tags

CCSS.HSF.LE.B.5

Front

How do you calculate the value of an item after depreciation?

Back

To calculate the value after depreciation, use the formula: Value = Initial Value * (1 - Decay Rate)^Time.

Front

What is the decay rate in the equation y = 5000(0.7)^x?

Back

The decay rate is 30%, meaning the quantity decreases by 30% each year.

Tags

CCSS.HSF-IF.C.8B

Front

What is the value of a car worth $28,000 after 5 years with a 15% annual depreciation?

Back

The value of the car after 5 years is $12,424.

Front

What does the equation y = a(1 + r)^x represent?

Back

This equation represents Exponential Growth, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is time.

Tags

CCSS.HSF-IF.C.8B

Front

If a sailboat costs $5,950 and depreciates by 11% per year, what will it be worth after 6 years?

Back

The sailboat will be worth $2,957.04 after 6 years.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula for calculating exponential decay?

Back

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

Tags

CCSS.HSF-IF.C.8B

Front

What is a common example of exponential decay in real life?

Back

A common example is the depreciation of vehicles, where their value decreases over time.

Front

What happens to a quantity in exponential decay?

Back

In exponential decay, the quantity decreases rapidly at first and then slows down over time.

Tags

CCSS.HSF-IF.C.8B