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, leading to rapid increases as time progresses.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to rapid decreases as time progresses.

Front

What does the variable 'a' represent in the formula y = a(1 + r)^t?

Back

The variable 'a' represents the initial amount or starting value before growth occurs.

Front

What does the variable 'r' represent in the formula y = a(1 + r)^t?

Back

The variable 'r' represents the growth rate expressed as a decimal.

Front

What does the variable 't' represent in the formula y = a(1 + r)^t?

Back

The variable 't' represents the time period over which the growth occurs.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is y = a(1 - r)^t.

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, where 'a' is the initial population, 'r' is the decay rate, and 't' is the number of years.

Front

If a population of 10,000 decreases by 10% each year, what will the population be after 1 year?

Back

The population after 1 year will be 9,000.

Front

What is the difference between linear growth and exponential growth?

Back

Linear growth increases by a fixed amount each period, while exponential growth increases by a fixed percentage, leading to larger increases over time.

Front

What is a real-world example of exponential growth?

Back

A common example is compound interest in finance, where the amount of interest earned grows over time based on the initial investment and interest rate.