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# Writing exponential functions from tables

Both linear equations and exponential equations represent relationships between two variables. However, the way that the variables are related to each other in each type of equation is different. A linear equation can be thought of as representing repeated addition on an initial value, while an exponential equation can be thought of as representing repeated multiplication on an initial value. Created by Sal Khan.

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• i didnt understand any of this
• If you don't get it, check the hints in the exercise. If you don't get it here are some examples.
x | f(x)
---------
0 | 4
1 | 8

So, we see that when x is 0, f(x) = 4. f(x) is like y. Then, when x=1, f(x)[or y] = 8. We see that we have to multiply 4 by 2 to get 8. So, f(x)=4*(2)^x. OR, y=4*(2)^x. And when we plug in x=1, We get f(x)=8, which is right based on the table. I hope this helps. If it doesn't, just comment.
• if Sal's got short memory then I dunno bout the rest of us
• 4 real.
• I dont really understand this pls help :(
• So Sal talks about two functions, linear (with a common difference) and exponential (with a common ratio). It is much easier when x is incremented by 1 such as shown (1, 2, 3, ...) because it is easier to find what we need. For linear equations, we have y = m (slope) x + b (y intercept) and for exponential equations we have y = a (initial value)*r(ratio or base)^x. So in each case, we need to find two things.
In both cases, the y intercept and initial value are found where x = 0 (y intercept) and the table gives us these, so linear b = 5 and exponential a = 3. We are already 1/2 way there.
Linear slope is found by the common difference (since slope is change in y/change in x and change in x is 1, divide by 1 does not change anything). We subtract any two consecutive terms 2nd - 1st which gives 7 -5 = 9 - 7 = 11 - 9 = ... = 2. So with a slope of 2 and an intercept of 5, we get y = 2x + 5.
For exponential, we divide instead of subtract, so 2/3 = (4/3)/2 = (8/9)/(4/3) = ... = 2/3. We have to use our dividing fraction skills to see they are the same, flip denominator and multiply, so 8/9 * 3/4 does reduce to 2/3 which gives us the base. So with an initial value of 3 and a base (common ratio) of 2/3 we get y = 3 (2/3)^x. I hope running them together makes more sense than separate since they can be related to each other is a variety of ways. Does this help?
• What do you do if you only have 2 points?
Here was the problem:
Complete the equation for the table:
h(x)=____
x___|0_|1
h(x)|10|4
I have h(x)=10*b^x. How do I find the exponential degree (b) if there are only two points? Thanks!
• Hi Kaitlyn,

You are almost there.
You already determined what happens if x = 0:
a·b⁰=10 <=> a·1=10 <=> a=10

Now do the same for x = 1, replacing "a" with 10:
10·b¹=4 <=> 10b=4 <=> b=4/10 <=> b=2/5

=> h(x)=10·(2/5)ˣ
(1 vote)
• Hey, so I came up with a good way to remember how to do this type of problem, so I'll give you an example to demonstrate.

x | f(x)
---------
0 | 9
1 | 15

So we have the first number, 9, become the second number, 15. a good trick to remember is if it is on the place where x=1, put that on the top. I call this "The Big Switcheroo." If it is on the top, put it on the bottom. So if we switch the 9 and the 15, we will get y=15/9^x. Any Questions?
• why does he do triangles when he says change for example at
• Those are not triangles, they are the Greek capital letter delta, which is the standard algebraic symbol for "change in".
• What do you do when you don't have the y-intercept?
• What about when you don't have the y-intercept? Not for the linear function, but the exponential one?
• I don't clearly understand this.