Basic 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, resulting in a rapid increase. For example, if a population doubles every year, it is experiencing exponential growth.

Front

What is exponential decay?

Back

Exponential decay occurs when a quantity decreases by a consistent percentage over a period of time, leading to a rapid decrease. An example is radioactive decay, where a substance loses half of its mass in a fixed time period.

Front

What is the general form of an exponential function?

Back

The general form of an exponential function is y = a * b^x, where 'a' is a constant, 'b' is the base (b > 0), and 'x' is the exponent.

Front

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

Back

In an exponential function y = a * b^x, the base 'b' represents the growth (b > 1) or decay (0 < b < 1) factor.

Front

How can you identify an exponential function from a graph?

Back

An exponential function graph will show a curve that either rises steeply (growth) or falls steeply (decay) rather than a straight line.

Front

What is the difference between linear and exponential functions?

Back

Linear functions increase or decrease by a constant amount, while exponential functions increase or decrease by a constant percentage.

Front

What is an example of a real-world situation that can be modeled by an exponential function?

Back

An example is compound interest in finance, where the amount of money grows exponentially over time due to interest being calculated on the accumulated amount.

Front

What is the y-intercept in an exponential function?

Back

The y-intercept of an exponential function y = a * b^x is the value of 'a', which represents the initial amount when x = 0.

Front

What happens to the graph of an exponential decay function as x increases?

Back

As x increases in an exponential decay function, the value of y approaches zero but never actually reaches it, creating a horizontal asymptote at y = 0.

Front

What is the formula for exponential decay?

Back

The formula for exponential decay can be expressed as y = a * e^(-kt), where 'a' is the initial amount, 'k' is the decay constant, and 't' is time.