Exponential Growth and Decay

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 10% each year, it will grow faster each subsequent year.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a consistent percentage over time. For example, if a substance loses 20% of its mass each year, it will decrease rapidly in the initial years.

Front

How do you convert a percentage to a decimal?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 11.2% becomes 0.112.

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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 (as a decimal), and 't' is time.

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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 (as a decimal), and 't' is time.

Front

What does the base of an exponential function represent?

Back

The base of an exponential function represents the growth or decay factor. For example, in f(x) = a(b)^x, 'b' indicates how much the quantity increases (if b > 1) or decreases (if 0 < b < 1).

Front

If a population of bacteria doubles every 3 hours, what type of growth is this?

Back

This is an example of Exponential Growth, as the population increases rapidly over time.

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What is the growth rate in the function f(x)=2(1.44)^x?

Back

The growth rate is 44%, as the base (1.44) indicates a 44% increase.

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How do you identify Exponential Growth vs. Exponential Decay?

Back

Exponential Growth has a base greater than 1 (e.g., 1.01), while Exponential Decay has a base between 0 and 1 (e.g., 0.7).

Front

Write the equation for a culture of bacteria that starts with 5000 cells and dies by 30% each year.

Back

The equation is y = 5000(0.7)^x, where 0.7 represents the 70% of cells remaining after a 30% decay.