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Algebra 1

Course: Algebra 1>Unit 12

Lesson 7: Exponential vs. linear models

Exponential growth & decay: FAQ

What's the difference between exponential and linear growth?

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 each day, while exponential growth might involve multiplying by 2 each day.

How can we tell if a graph represents exponential or linear growth?

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.

What's the difference between exponential growth and exponential decay?

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.

How do we create an exponential function from a table or graph?

There are a few steps to this. First, identify the initial value (the 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, equals, a, left parenthesis, b, right parenthesis, start superscript, x, end superscript, where a is the initial value and b is the growth or decay factor.

Where do we see exponential growth and decay in the real world?

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

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• How do you graph exponential functions? The video was not very helpful.