Exponential Growth & 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 growth as time progresses.

Front

What is Exponential Decay?

Back

Exponential Decay occurs when a quantity decreases by a consistent percentage over time, leading to a rapid decrease as time progresses.

Front

What does the variable 'a' represent in the equation y = a(1 + r)^x?

Back

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

Front

Write the equation for a population that starts at 200 and grows at a rate of 10% per year.

Back

y = 200(1.10)^x

Front

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

Back

The growth factor is 0.80 (1 - 0.20).

Front

How do you calculate the future value of an investment with exponential growth?

Back

Use the formula: Future Value = Initial Amount * (1 + Growth Rate)^Number of Periods.

Front

What is the difference between linear growth and exponential growth?

Back

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

Front

If a population of bacteria doubles every hour, what type of growth is this?

Back

This is an example of exponential growth.

Front

Write the equation for a quantity that starts at 50 and decays at a rate of 15% per year.

Back

y = 50(0.85)^x

Front

What is the formula for calculating exponential decay?

Back

The formula is: y = a(1 - r)^x, where 'a' is the initial amount and 'r' is the decay rate.