Exponential Growth & Decay

Front

What is exponential growth?

Back

Exponential growth occurs when the growth rate of a value is proportional to its current value, leading to growth that accelerates over time.

Front

What is exponential decay?

Back

Exponential decay is the process by which a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease that slows over time.

Front

What is the general formula for exponential growth?

Back

The general 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

What is the general formula for exponential decay?

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The general 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 does the y-intercept represent in an exponential function?

Back

The y-intercept represents the initial value of the function when time (t) is zero.

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How can you identify exponential growth on a graph?

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Exponential growth is identified by a curve that rises steeply and continuously increases as it moves to the right.

Front

How can you identify exponential decay on a graph?

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Exponential decay is identified by a curve that decreases rapidly and approaches zero as it moves to the right.

Front

What is the significance of the base in an exponential function?

Back

The base of an exponential function determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

How do you calculate the population after a certain time in exponential growth?

Back

To calculate the population after a certain time in exponential growth, use the formula y = a(1 + r)^t, substituting the initial population for 'a', the growth rate for 'r', and the time for 't'.

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What is a common application of exponential growth in real life?

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A common application of exponential growth is in population studies, where populations can grow rapidly under ideal conditions.