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)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Tags

CCSS.HSF-IF.C.8B

Front

How do you calculate the remaining amount after exponential decay?

Back

To calculate the remaining amount after exponential decay, use the formula: Remaining Amount = Initial Amount * (1 - Decay Rate)^Time.

Front

What is the decay rate in the context of exponential decay?

Back

The decay rate is the percentage at which a quantity decreases over a specific time period, expressed as a decimal in calculations.

Tags

CCSS.HSF-IF.C.8B

Front

If a substance decays by 30% each hour, what is the decay rate?

Back

The decay rate is 0.30 (or 30%).

Tags

CCSS.HSF-LE.A.1C

Front

How much ibuprofen is left after 3 hours if 200 mg is taken and it decays by 30% each hour?

Back

68.6 mg.

Tags

CCSS.HSF.BF.A.2

Front

What is the formula for calculating the value of a depreciating asset?

Back

The formula is: Value = Initial Cost * (1 - Depreciation Rate)^Years.

Front

If a boat costs $7650 and depreciates at 14% per year, what is the value after 3 years?

Back

The value after 3 years is approximately $3,800.34.

Tags

CCSS.HSF.BF.A.2

Front

What does the equation y = 10,000(0.76)^x represent?

Back

This equation represents exponential decay, as the base (0.76) is less than 1.

Tags

CCSS.HSF-IF.C.8B

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value, while exponential decay occurs when it decreases at a rate proportional to its current value.

Tags

CCSS.HSF-IF.C.8B

Front

How do you determine if an equation represents growth or decay?

Back

If the base of the exponential function is greater than 1, it represents growth; if it is between 0 and 1, it represents decay.

Tags

CCSS.HSF-IF.C.8B