Exponential growth

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.

Front

What is the difference between exponential growth and exponential decay?

Back

Exponential growth occurs when a quantity increases at a consistent percentage rate over time, while exponential decay occurs when a quantity decreases at a consistent percentage rate.

Front

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

Back

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

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 exponential decay if a quantity decreases by 20% each period.

Back

y = a(0.8)^x, where 'a' is the initial amount.

Front

What is the formula for calculating exponential growth?

Back

The formula is y = a(1 + r)^x, where 'a' is the initial amount, 'r' is the growth rate, and 'x' is the time period.

Front

What does the base 'b' in an exponential function indicate?

Back

The base 'b' indicates the growth factor; if b > 1, it represents growth, and if 0 < b < 1, it represents decay.

Front

How do you identify an exponential decay function from its equation?

Back

An exponential decay function has a base between 0 and 1, such as y = a(0.5)^x.

Front

What is the growth rate in the equation y = 6(1.14)^x?

Back

The growth rate is 14%, as indicated by the (1 + r) where r = 0.14.

Front

If a quantity decreases from 100 to 80 in one time period, what is the decay factor?

Back

The decay factor is 0.8, calculated as 80/100.