Exponential Growth and Decay

Front

What is Exponential Growth?

Back

Exponential Growth occurs when a quantity increases by a fixed percentage over a period of time, leading to rapid increases as the base amount grows.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a fixed percentage over a period of time, leading to rapid decreases as the base amount shrinks.

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

How do you calculate the decay factor from a decay rate of 20%?

Back

The decay factor is 1 - 0.20 = 0.80.

Front

If a population of 8,000 fish decreases by 6% per year, what is the population after 10 years?

Back

The population after 10 years is approximately 4,309.

Front

What does the term 'common ratio' refer to in exponential functions?

Back

The common ratio is the factor by which a quantity multiplies during each time period in exponential growth or decay.

Front

For the function f(x) = 300(1.16)^x, what is the common ratio?

Back

The common ratio is 1.16.

Front

What is the significance of the base in an exponential function?

Back

The base determines the rate of growth or decay; a base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.

Front

How does depreciation relate to exponential decay?

Back

Depreciation is a form of exponential decay where an asset loses value at a constant percentage rate over time.