Exponential Growth and Decay Word Problems

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a fixed percentage over a period of time, resulting in a rapid increase as time progresses.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to a rapid decrease as time progresses.

Front

What is the general formula for exponential growth?

Back

Front

What is the general formula for exponential decay?

Back

Front

How do you convert a percentage rate to a decimal for calculations?

Back

To convert a percentage to a decimal, divide the percentage by 100. For example, 2.7% becomes 0.027.

Front

If a population of 15000 decreases by 1.5% each year, what is the decay factor?

Back

The decay factor is 0.985, calculated as 1 - 0.015.

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Back

The 'a' value represents the initial amount or starting quantity before growth or decay occurs.

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Back

0.98625 represents the decay factor, indicating a decrease of 1.375% per hour.

Front

What is the difference between growth and decay in terms of the base of the exponent?

Back

In growth, the base is greater than 1 (e.g., 1.02), while in decay, the base is less than 1 (e.g., 0.98).

Front

How can you determine if a function represents growth or decay?

Back

If the growth rate (r) is positive, it represents growth; if the decay rate (r) is negative, it represents decay.