Exponential growth & decay: FAQ

In linear growth, we add or subtract the same amount each time period, while in exponential growth, we multiply by the same factor each time period. For example, linear growth might involve adding $5$5 each day, while exponential growth might involve multiplying by $2$2 each day.

Practice with our Exponential vs. linear growth exercise.

One of the hallmarks of exponential growth is that the graph will get steeper and steeper over time. Linear growth, on the other hand, will have a constant slope.

Practice with our Graphs of exponential growth exercise.

While both involve exponential functions, exponential growth refers to when the quantity is increasing over time, while exponential decay refers to when the quantity is decreasing over time.

Practice with our Exponential growth vs. decay exercise.

There are a few steps to this. First, identify the initial value (the $y$y-intercept). Second, determine whether the function is growing or decaying. Third, find the growth or decay factor - this will be the number we're multiplying by each time period. Once we have these three pieces of information, we can write the exponential function in the form $y = a(b)^x$y, equals, a, left parenthesis, b, right parenthesis, start superscript, x, end superscript, where $a$a is the initial value and $b$b is the growth or decay factor.

Practice with our Exponential functions from tables & graphs exercise.

There are many examples! Compound interest is a common example of exponential growth, while radioactive decay is a common example of exponential decay.

Practice with our Connecting exponential graphs with contexts exercise.