Exponential Growth and Decay

Front

What is an exponential function?

Back

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases by a constant percentage over time, while exponential decay occurs when a quantity decreases by a constant percentage over time.

Front

What is the general form of an exponential growth equation?

Back

Front

What is the general form of an exponential decay equation?

Back

Front

If a population of bacteria doubles every hour, what type of function does this represent?

Back

This represents exponential growth.

Front

How do you convert a percentage growth rate into a growth factor?

Back

To convert a percentage growth rate 'r' into a growth factor, use the formula: Growth Factor = 1 + r (as a decimal). For example, a 14% growth rate becomes 1.14.

Front

What is the growth factor for a 35% increase?

Back

The growth factor for a 35% increase is 1.35.

Front

If a quantity decreases by 20% each year, what is the decay factor?

Back

The decay factor is 0.80 (since 1 - 0.20 = 0.80).

Front

Write an equation for a quantity that starts at 100 and decreases by 10% each year.

Back

Front

What does the base of an exponential function represent?

Back

The base of an exponential function represents the growth or decay factor. If the base is greater than 1, it indicates growth; if it is between 0 and 1, it indicates decay.