Exponential Growth & 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: A population of bacteria doubles every hour.

Front

What is Exponential Decay?

Back

Exponential decay is the decrease of a quantity at a rate proportional to its current value, leading to a rapid decline. Example: A radioactive substance decays by 5% each year.

Front

Define the Common Ratio in exponential functions.

Back

The common ratio is the factor by which a quantity multiplies during each time period in exponential growth or decay. Example: In the function y = a(r)^x, r is the common ratio.

Front

What is the formula for Exponential Growth?

Back

The formula for exponential growth is y = a(1 + r)^t, where 'a' is the initial amount, 'r' is the growth rate, and 't' is time.

Front

What is the formula for Exponential Decay?

Back

The formula for exponential decay is y = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

How do you calculate the population after a certain number of years with exponential decay?

Back

Use the formula y = a(1 - r)^t, substituting 'a' for the initial population, 'r' for the decay rate, and 't' for the number of years.

Front

What does a Common Ratio of 1 indicate?

Back

A common ratio of 1 indicates that the quantity remains constant over time, showing no growth or decay.

Front

If a quantity decreases by 30% each year, what is the common ratio?

Back

The common ratio is 0.7, calculated as 1 - 0.30.

Front

Write the equation for a population that starts at 8000 and decreases by 6% per year.

Back

y = 8000(0.94)^t.

Front

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

Back

The base indicates the growth or decay factor. A base greater than 1 indicates growth, while a base between 0 and 1 indicates decay.