In Exercises 61–64, give the equation of each exponential functio...

Question

In Exercises 61–64, give the equation of each exponential function whose graph is shown.

Graph of an exponential function with points (0,2), (1,4), and (2,8).

Graph of an exponential function with points (0,1), (1,4), and (2,16).

Accepted Answer

Hey everyone in this problem we are asked which of the following exponential functions represents the graph given below. Okay. And the graph given below here shown in blue and we're giving kind of three points on that graph. 0214 and 28. Okay. Alright. So we want to write an exponential function representing this graph but we know that in general an exponential function has a following form, Y is equal to C times B to the exponent X. Okay, so B as the base. Um and then we have this kind of constant ceo Open front. All right. Well, in order to write an exponential function, we need to find C and we need to find B. Okay, so we have two unknowns but we actually have three points. Okay, so having two unknowns and three points, we're gonna be able to do this and we'll only actually need two points in order to figure out what C and B is. Okay, so let's start with .02. Okay, if we substitute into And let's call this equation star. Okay, so what's sub 02 into this equation? What you're gonna find? We get two is equal to C times B to the exponent zero. We'll be to the experiment, zero is just one. So we get to see Is equal to two. Alright, so this see value. Okay, if you didn't recall previously you stub in this point this see value represents the Y intercept where the function crosses that Y axis because that's when X is zero and then this B to the X. Goes just to one. Okay so C. Is always gonna be that Y intercept in your exponential function. Okay so we know that C. Is equal to two. So now we have Y. Is equal to two times B to the exponent X. Now we're gonna do red star here and we'll label this with the red star because it has a little bit more information than that blue function. And now we need to figure out what is B. And again we have two other points. 14 and 28. You can choose either of them. Okay we're going to substitute another point because we have that gives us a Y value and an X value and then we'll be able to solve for B. Okay so let's substitute into The Red Star Equation. And again you can use either point which is in 14 We're gonna get four is equal to two time speed. To the experiment. Okay? And if you're given points, try to choose the ones that make things easier. In this case the X value is one. So we just got beat to the exponent one. We don't have to do any like square rooting or anything like that. We just have to divide by two. So that one's a little bit simpler. So if you have a choice try to choose the one that's gonna make life simpler for you. Alright so be to the exponent one is just be we divide by two and we get that B. Is equal to two. Okay? So now we have our C. Value and we have our B. Value and we can write that our function is going to be Y. Is equal to C. Which we found to be two times B. We found to be to the exponent X. So our exponential function that represents this graph is going to be why is equal to two times two to the exponent X. That's going to be answer. C. Thanks everyone for watching. I hope this video helped see you in the next one.

In Exercises 61–64, give the equation of each exponential function whose graph is shown.

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