What is difference between linear increae and exponential increase?
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A linear function is one that is changing at a constant rate as changes. An exponential function is one that changes at a rate that's always proportional to the value of the function.
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What is the difference between Linear and exponential functions?
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James Brust, Lecturer (Mathematics) at California State University, San Marcos
Answered Jan 3, 2017
“Linear function” can mean a couple of things. But in the context of high-school-level algebra, the basic ideas are like this:
A linear function is one that is changing at a constant rate as xxchanges.
An exponential function is one that changes at a rate that's always proportional to the value of the function. A simple example is population growth for a very simple kind of organism, like bacteria. The larger the population is, the more the population will increase. (This is also assuming that the population hasn't gotten too large for its habitat.)
That might not seem so clear, but the difference between them might be easier to see if you look at the values of f(0),f(1),f(2),f(3),f(0),f(1),f(2),f(3), and so on.
First let's look at the general formulas:
Linear: f(x)=ax+bf(x)=ax+b. (You'll probably often see it as f(x)=mx+bf(x)=mx+b, but let's stick with ax+bax+b so we can see the parallels between these concepts more easily.)
Exponential: f(x)=baxf(x)=bax, where aais a positive number other than 11.
When you look at the linear function and compare f(0),f(1),f(2),f(3),…f(0),f(1),f(2),f(3),…, you may notice that when you add aa to f(0)f(0) you get f(1)f(1). When you add aa to f(1)f(1) you get f(2)f(2). When you add aa to f(2)f(2) you get f(3)f(3), and so on. Each time you increase xx by 11, f(x)f(x) gets aa added to it.
(In this case, f(0),f(1),f(2),f(3),…f(0),f(1),f(2),f(3),…form what we call an arithmetic sequence.)
The exponential function has a related idea going on. When you multiply f(0)f(0) by aa you get f(1)f(1), and it goes on like that.
(In this case, f(0),f(1),f(2),f(3),…f(0),f(1),f(2),f(3),…form what we call a geometric sequence.)
Another thing you might notice, from playing around with these different functions, is that in both cases, bb is the “starting” value. In other words, f(0)=
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6 ANSWERS

James Brust, Lecturer (Mathematics) at California State University, San Marcos
Answered Jan 3, 2017
“Linear function” can mean a couple of things. But in the context of high-school-level algebra, the basic ideas are like this:
A linear function is one that is changing at a constant rate as xxchanges.
An exponential function is one that changes at a rate that's always proportional to the value of the function. A simple example is population growth for a very simple kind of organism, like bacteria. The larger the population is, the more the population will increase. (This is also assuming that the population hasn't gotten too large for its habitat.)
That might not seem so clear, but the difference between them might be easier to see if you look at the values of f(0),f(1),f(2),f(3),f(0),f(1),f(2),f(3), and so on.
First let's look at the general formulas:
Linear: f(x)=ax+bf(x)=ax+b. (You'll probably often see it as f(x)=mx+bf(x)=mx+b, but let's stick with ax+bax+b so we can see the parallels between these concepts more easily.)
Exponential: f(x)=baxf(x)=bax, where aais a positive number other than 11.
When you look at the linear function and compare f(0),f(1),f(2),f(3),…f(0),f(1),f(2),f(3),…, you may notice that when you add aa to f(0)f(0) you get f(1)f(1). When you add aa to f(1)f(1) you get f(2)f(2). When you add aa to f(2)f(2) you get f(3)f(3), and so on. Each time you increase xx by 11, f(x)f(x) gets aa added to it.
(In this case, f(0),f(1),f(2),f(3),…f(0),f(1),f(2),f(3),…form what we call an arithmetic sequence.)
The exponential function has a related idea going on. When you multiply f(0)f(0) by aa you get f(1)f(1), and it goes on like that.
(In this case, f(0),f(1),f(2),f(3),…f(0),f(1),f(2),f(3),…form what we call a geometric sequence.)
Another thing you might notice, from playing around with these different functions, is that in both cases, bb is the “starting” value. In other words, f(0)=
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