Exponential Growth and Decay

Front

What is exponential growth?

Back

Exponential growth occurs when a quantity increases by a consistent percentage over a period of time, resulting in a rapid increase in value.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease in value.

Front

What is the general form of an exponential function?

Back

The general form is f(x) = a(b)^x, where 'a' is the initial amount, 'b' is the growth (b > 1) or decay factor (0 < b < 1), and 'x' is the time.

Front

What does the term 'initial amount' refer to in an exponential function?

Back

The initial amount is the value of the function when x = 0, represented by 'a' in the function f(x) = a(b)^x.

Front

How do you determine the growth factor from an exponential function?

Back

The growth factor is the base 'b' in the function f(x) = a(b)^x, where b > 1 indicates growth.

Front

How do you determine the decay factor from an exponential function?

Back

The decay factor is the base 'b' in the function f(x) = a(b)^x, where 0 < b < 1 indicates decay.

Front

What is the formula to calculate the decay factor from a percentage rate?

Back

The decay factor can be calculated using the formula (1 - r), where r is the rate of decay expressed as a decimal.

Front

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

Back

The decay factor is 0.80, calculated as (1 - 0.20).

Front

What is the relationship between growth rate and growth factor?

Back

The growth factor can be calculated as (1 + r), where r is the growth rate expressed as a decimal.

Front

If a quantity increases by 15% each year, what is the growth factor?

Back

The growth factor is 1.15, calculated as (1 + 0.15).