The data in the table can be modeled using an exponential function. x −1 0 1 2 3
y 2 5 12.5 31.25 78.125
Based on the table, which function represents the same relationship?

f(x)=2.5x

f(x)=2⋅0.4x

f(x)=5⋅2.5x

f(x)=5⋅0.4x

f(x)=5⋅2.5^x

Step-by-step explanation:

Simple really, all you have to do is plug it in.

5·2.5 ^(-1)

Once you plug it in, solve it! This part you can do on a calculator, or you could always solve it out.  

The answer is 2. So that one was correct because 5⋅2.5^(-1) = 2 like the graph says, -1x = 2y. You still have to make sure that it is correct all the way through. So, just plug in the x value in the (x) spot.

The x values are:

-1, 0, 1, 2, and 3

The y values (which are the answers) are:

2, 5, 12.5, 31.25, and 78.125.

Every time you plug in the numbers, make sure you place them in the right spot. For instance, 5⋅2.5^x is the equation; all you have to do is put the x values in the x spot to get the answer.

The next value 5⋅2.5^(0) equals to 5. If the answers come out the same as the graph; it means its correct.

The other answers are NOT correct because the answer is not the same as the y values.

I want to make this as simple as possible so let me break it down. F(x) is just telling you to plug the equation in. The graph is telling you what numbers to plug in and what the answer should be. The x value is going to be the number you plug in. You just need to put it in the (x) spot (where ever it says (x) that's where you need to plug it in.) The y value is what your answer should be, if it is not your answer, that means it's not correct. An easy way to get the answers is by going through the answer choses and plugging them in as that. So what I did was take the equation f(x)=5⋅2.5^x and plug it in as that. Yes, I did go through all the other ones like f(x)= 2.5^x, but it was way easier to do. Just make sure you check through them all, so you don't mess up.

step-by-step explanation:

the discriminant is 64 + 4*1*12 = 112

this is prime.

step-by-step explanation: