Exponential Growth or Decay?

Front

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.

Front

What is exponential decay?

Back

Exponential decay describes a process where a quantity decreases at a rate proportional to its current value, resulting in a rapid decrease that slows over time.

Front

How is the half-life of a substance defined?

Back

The half-life is the time required for a quantity to reduce to half its initial amount, commonly used in radioactive decay.

Front

What is the formula for exponential growth?

Back

The formula is: N(t) = N0 * e^(rt), where N(t) is the amount at time t, N0 is the initial amount, r is the growth rate, and e is Euler's number.

Front

What is the formula for exponential decay?

Back

The formula is: N(t) = N0 * e^(-rt), where N(t) is the amount at time t, N0 is the initial amount, r is the decay rate, and e is Euler's number.

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What does a positive growth rate indicate?

Back

A positive growth rate indicates that a quantity is increasing over time.

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What does a negative growth rate indicate?

Back

A negative growth rate indicates that a quantity is decreasing over time.

Front

What is an example of exponential growth in real life?

Back

An example of exponential growth is the spread of a viral infection, where each infected person can infect multiple others.

Front

What is an example of exponential decay in real life?

Back

An example of exponential decay is the depreciation of a car's value over time.

Front

How does population growth relate to exponential functions?

Back

Population growth can often be modeled using exponential functions when the growth rate is constant.