Log in calvertb24 4 years agoPosted 4 years ago. Direct link to calvertb24's post “i didnt understand any of...” i didnt understand any of this • (32 votes) Coogle Chess 3 years agoPosted 3 years ago. Direct link to Coogle Chess's post “If you don't get it, chec...” If you don't get it, check the hints in the exercise. If you don't get it here are some examples. 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. (5 votes) summer_duck a year agoPosted a year ago. Direct link to summer_duck's post “if Sal's got short memory...” if Sal's got short memory then I dunno bout the rest of us • (15 votes) GlubTub 2 months agoPosted 2 months ago. Direct link to GlubTub's post “4 real.” 4 real. (0 votes) For Kobe, aka sad 2020 :( 4 years agoPosted 4 years ago. Direct link to For Kobe, aka sad 2020 :('s post “I dont really understand ...” I dont really understand this pls help :( • (6 votes) David Severin 4 years agoPosted 4 years ago. Direct link to David Severin's post “So Sal talks about two fu...” 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. (3 votes) kaitlyn 4 years agoPosted 4 years ago. Direct link to kaitlyn's post “What do you do if you onl...” What do you do if you only have 2 points? • (3 votes) Nights Dawn 4 years agoPosted 4 years ago. Direct link to Nights Dawn's post “Hi Kaitlyn,You are almo...” Hi Kaitlyn, You are almost there. Now do the same for x = 1, replacing "a" with 10: (2 votes) P Nicholas 9 years agoPosted 9 years ago. Direct link to P Nicholas's post “why does he do triangles ...” why does he do triangles when he says change for example at • (0 votes) Just Keith 9 years agoPosted 9 years ago. Direct link to Just Keith's post “Those are not triangles, ...” Those are not triangles, they are the Greek capital letter delta, which is the standard algebraic symbol for "change in". (8 votes) Amie.Anderegg 8 years agoPosted 8 years ago. Direct link to Amie.Anderegg's post “What do you do when you d...” What do you do when you don't have the y-intercept? • (2 votes) Louis MN 8 years agoPosted 8 years ago. Direct link to Louis MN's post “What about when you don't...” What about when you don't have the y-intercept? Not for the linear function, but the exponential one? (2 votes) sophia a year agoPosted a year ago. Direct link to sophia's post “I dont get this can someo...” I dont get this can someone please help • (1 vote) Wesley a year agoPosted a year ago. Direct link to Wesley's post “Hey, so I came up with a ...” 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) 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? (3 votes) r.ninja.2018 6 months agoPosted 6 months ago. Direct link to r.ninja.2018's post “I don't clearly understan...” I don't clearly understand this. • (2 votes) rita200777 a year agoPosted a year ago. Direct link to rita200777's post “how do we write a exponen...” how do we write a exponential equations • (2 votes) Mango a year agoPosted a year ago. Direct link to Mango's post “An exponential equation i...” An exponential equation is an equation that has a x as the exponent. If when x is 0 and y is not 1, that means there is a multiplier. The multiplier is equal to the y-intercept. (1 vote) MasonG 8 years agoPosted 8 years ago. Direct link to MasonG's post “I don't get something: Wh...” I don't get something: Why did Sal do 'Δf/Δx' instead of just solving 'mx + b' for 'x' like 'm1 + 5 = 7', '(2)1 + 5 = 7', so 'm = 2'? • (1 vote) Johnathan 8 years agoPosted 8 years ago. Direct link to Johnathan's post “The use of `Δf/Δx` is the...” The use of (3 votes)Want to join the conversation?
x | f(x)
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0 | 4
1 | 8
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?
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!
You already determined what happens if x = 0: a·b⁰=10 <=> a·1=10 <=> a=10 10·b¹=4 <=> 10b=4 <=> b=4/10 <=> b=2/5=> h(x)=10·(2/5)ˣ
1:30
---------
0 | 9
1 | 15
If the y-value is decreasing, then it's called exponential decay and the base of x must be smaller than 1.Δf/Δx is the standard form of finding the slope. It is good for those times when you don't know the value of x and y.
Video transcript
Consider the following tableof values for a linear function f of x is equal to mx plus band an exponential function g of x is equal to atimes r to the x. Write the equationfor each function. And so they give us,for each x-value, what f of x is andwhat g of x is. And we need to figure out theequation for each function and type them in over here. So I copy andpasted this problem on my little scratchpad. So let's first thinkabout the linear function. And to figure out theequation of a line or a linear functionright over here, you really just need two points. And I always like to use thesituation when x equals 0 because that makesit very clear what the y-intercept is going to be. So, for example, wecan say that f of 0 is going to be equalto m times 0 plus b. Or this is just goingto be equal to b. And they tell us thatf of 0 is equal to 5. b is equal to 5. So we immediately knowthat this b right over here is equal to 5. Now, we just haveto figure out the m. We have to figure outthe slope of this line. So just as a little bitof a refresher on slope, the slope of this line isgoing to be our change in y-- or our change in our functionI guess we could say, if we say that thisy is equal to f of x-- over our change in x. And actually, let mewrite it that way. We could writethis as our change in our functionover our change in x if you want to lookat it that way. So let's look atthis first change in x when x goes from 0 to 1. So we finish at 1. We started at 0. And f of x finishesat 7 and started at 5. So when x is 1, f of x is 7. When x is 0, f of x is 5. And we get a changein our function of 2 when x changes by 1. So our m is equal to 2. And you see that. When x increases by 1, ourfunction increases by 2. So now we know theequation for f of x. f of x is going to be equalto 2 times 2x plus b, or 5. So we figured outwhat f of x is. Now we need to figureout what g of x is. So g of x is anexponential function. And there's really two thingsthat we need to figure out. We need to figureout what a is, and we need to figure out what r is. And let me just rewrite that. So we know that g of x--maybe I'll do it down here. g of x is equal to atimes r to the x power. And if we know what g of 0 is,that's a pretty useful thing. Because r to the 0thpower, regardless of what r is-- orI guess we could assume that r is not equal to 0. People can debate what0 to the 0 power is. But if r is anynon-zero number, we know that if you raise itto the 0 power, you get 1. And so thatessentially gives us a. So let's just write that down. g of 0 is a times r tothe 0 power, which is just going to be equalto a times 1 or a. And they tell us what g of0 is. g of 0 is equal to 3. So we know that a is equal to 3. So so far, we know that our gof x can be written as 3 times r to the x power. So now we can just use anyone of the other values they gave us to solve for r. For example, they tell usthat g of 1 is equal to 2. So let's writethat down. g of 1, which would be 3 times r tothe first power, or just 3-- let me just write it. It could be 3 timesr to the first power, or we could just writethat as 3 times r. They tell us that gof 1 is equal to 2. So we get 3 timesr is equal to 2. Or we get that ris equal to 2/3. Divide both sides ofthis equation by 3. So r is 2/3. And we're done. g of x is equal to 3 times 2/3. Actually, let me justwrite it this way. 3 times 2/3 to the x power. You could write it that wayif you want, any which way. So 3 times 2/3 to the x power,and f of x is 2x plus 5. So let's actuallyjust type that in. So f of x is 2x plus 5. And we can verify that that'sthe expression that we want. And g of x is 3 times 2over 3 to the x power. And let me just verify thatthat's what I did there. I have a short memory. All right. Yeah, that looks right. All right. Let's check our answer. And we got it right.
