Exponential Growth and Decay

Front

What is exponential growth?

Back

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

Front

What is exponential decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, resulting in a rapid decline that slows over time.

Front

What is linear decay?

Back

Linear decay refers to a constant decrease in a quantity over time, represented by a straight line on a graph.

Front

How can you identify exponential growth on a graph?

Back

Exponential growth is identified by a smooth curve that rises steeply as time progresses.

Front

How can you identify exponential decay on a graph?

Back

Exponential decay is identified by a smooth curve that decreases rapidly at first and then levels off.

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.

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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 is the difference between exponential and linear functions?

Back

Exponential functions grow or decay at rates proportional to their current value, while linear functions change at a constant rate.

Front

What are some real-world examples of exponential growth?

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Examples include population growth, compound interest, and the spread of diseases.

Front

What are some real-world examples of exponential decay?

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Examples include radioactive decay, depreciation of assets, and cooling of hot objects.