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, resulting in a rapid increase as the quantity 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 a rapid decrease as the quantity diminishes.

Front

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

Back

Future Value = Present Value * (1 + growth rate)^number of years.

Front

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

Back

Future Value = Present Value * (1 - decay rate)^number of years.

Front

What is the formula for exponential growth?

Back

f(t) = 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

f(t) = a(1 - r)^t, where 'a' is the initial amount, 'r' is the decay rate, and 't' is time.

Front

What does the variable 'a' represent in the exponential function?

Back

The variable 'a' represents the initial value or starting amount in the exponential function.

Front

What does the variable 'r' represent in the exponential function?

Back

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

Front

How can you determine if a function represents growth or decay?

Back

If the growth rate (r) is positive, it represents growth; if the decay rate (r) is negative, it represents decay.

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.