Exponential Growth and Decay

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What is Exponential Growth?

Back

Exponential growth occurs when the increase in a quantity is proportional to its current value, leading to growth at an increasing rate over time.

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What is Exponential Decay?

Back

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time, leading to a decrease that slows down as the quantity decreases.

Front

What does the variable 'a' represent in exponential equations?

Back

In exponential equations, 'a' represents the initial amount or starting value before any growth or decay occurs.

Front

What does the variable 'r' represent in exponential equations?

Back

In exponential equations, 'r' represents the rate of growth or decay expressed as a decimal.

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How do you convert a percentage to a decimal?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 5% becomes 0.05.

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What is the formula for exponential decay?

Back

The formula for exponential decay is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

What is the formula for exponential growth?

Back

The formula for exponential growth is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

If a population decreases by 5% per year, what is the decay factor?

Back

The decay factor is 0.95, which represents the remaining population after a 5% decrease.

Front

If a boat depreciates by 12% per year, what is the value of the boat after 1 year?

Back

The value after 1 year is calculated as y = 25000(0.88)^1 = $22,000.

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What is the value of a population of 5,000 after 2 years if it decreases by 5% per year?

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The value after 2 years is calculated as y = 5000(0.95)^2 = $4,507.50.