Exponential Decay Applications

Front

What is Exponential Decay?

Back

Exponential decay is a process where a quantity decreases at a rate proportional to its current value, often modeled by the equation y = 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 the formula for calculating the value of an asset after depreciation?

Back

The formula is y = a(1 - r)^x, where 'y' is the value after 'x' years, 'a' is the initial value, 'r' is the depreciation rate, and 'x' is the number of years.

Front

How do you calculate the depreciation of an asset?

Back

To calculate depreciation, multiply the initial value by the decay factor (1 - r) raised to the power of the number of years: y = a(1 - r)^x.

Front

What does a decay factor of 0.86 represent?

Back

A decay factor of 0.86 indicates a 14% depreciation rate, meaning the asset retains 86% of its value each year.

Tags

CCSS.HSF-IF.C.8B

Front

What is half-life in the context of exponential decay?

Back

Half-life is the time required for a quantity to reduce to half its initial value, commonly used in radioactive decay.

Front

If a car is worth $20,000 and depreciates at 10% per year, what is the equation for its value?

Back

y = 20,000(0.90)^x.

Tags

CCSS.HSF.LE.A.2

Front

What is the significance of the base in an exponential decay equation?

Back

The base in an exponential decay equation (1 - r) indicates the proportion of the quantity that remains after each time period.

Tags

CCSS.HSF-IF.C.8B

Front

How can you determine the remaining mass of a substance after several years of decay?

Back

Use the formula y = a(0.5)^x for half-life decay, where 'a' is the initial mass and 'x' is the number of years.

Front

What does the graph of an exponential decay function look like?

Back

The graph of an exponential decay function decreases rapidly at first and then levels off, approaching zero but never actually reaching it.

Tags

CCSS.HSF-IF.C.7E

Front

What is the relationship between exponential decay and real-world applications?

Back

Exponential decay models are used in various fields, including finance (depreciation), biology (population decline), and physics (radioactive decay).