Exponential Growth and Decay

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form f(x) = a * b^x, where 'a' is a constant, 'b' is a positive real number, and 'x' is the exponent. It shows rapid growth or decay.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases at a rate proportional to its current value (b > 1). Exponential decay occurs when a quantity decreases at a rate proportional to its current value (0 < b < 1).

Front

What is the initial value in an exponential function?

Back

The initial value in an exponential function is the value of the function when x = 0, represented by 'a' in the function f(x) = a * b^x.

Front

How do you determine if a function represents exponential growth or decay?

Back

If the base 'b' in the function f(x) = a * b^x is greater than 1, it represents exponential growth. If 'b' is between 0 and 1, it represents exponential decay.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay is f(t) = 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 P = P0 * (1 - r)^t, where P0 is the initial population, r is the decay rate, and t is the number of years.

Front

What is the formula for exponential growth?

Back

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

Front

If a quantity doubles every year, what is the growth factor?

Back

The growth factor is 2, meaning the quantity increases by 100% each year.

Front

What does a decay rate of 20% per hour mean?

Back

It means that every hour, 20% of the current amount is lost, leaving 80% remaining.

Front

How do you find the value of a depreciating asset after several years?

Back

Use the formula V = P * (1 - r)^t, where V is the value after t years, P is the initial value, r is the depreciation rate, and t is the number of years.