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. Example: Population growth where the population doubles at regular intervals.

Front

What is Exponential Decay?

Back

Exponential decay describes the process of reducing an amount by a consistent percentage rate over a period of time. Example: Radioactive decay of a substance.

Front

What is the formula for Exponential Growth?

Back

The formula is: A = P(1 + r)^t, where A is the amount after time t, P is the initial amount, r is the growth rate, and t is time.

Front

What is the formula for Exponential Decay?

Back

The formula is: A = P(1 - r)^t, where A is the amount after time t, P is the initial amount, r is the decay rate, and t is time.

Front

What is a Growth Factor?

Back

The growth factor is the amount by which a quantity increases in each time period. It is calculated as 1 + growth rate.

Front

What is a Decay Factor?

Back

The decay factor is the amount by which a quantity decreases in each time period. It is calculated as 1 - decay rate.

Front

If the growth rate is 80%, what is the growth factor?

Back

1.8

Front

If the decay rate is 20%, what is the decay factor?

Back

0.8

Front

What does the y-intercept represent in the equation y = 4^x?

Back

The y-intercept is the value of y when x = 0. For y = 4^x, the y-intercept is 1.

Front

How do you identify Exponential Growth from an equation?

Back

If the base of the exponent is greater than 1, the model represents exponential growth. Example: A = 10(1.01)^t.