Find the equation of the exponential function represented by the table below:

Step-by-step explanation:

The exponential function is .   is the initial value of the function, or the y-value when x=0. In this case, =5. If we enter that into the equation:

Then we can use another point to solve for .

Since anything raised to the power of 1 remains the same, we can continue to solve algebraically.

Now that we have both the and value, we can return to the exponential function and fill in the blanks.

I hope this helps!

step-by-step explanation:

the triangles are similar. therefore the corresponding sides are in proportion:

              cross multiply

            divide both sides by 32

let's call the solutions x₁ = (5 - 2√7)/3 and x₂ = (5 + 2√7)/3

then the equation is (x-x₁)(x-x₂) = 0

if you fill that in you get a lot of numbers which you can recognize as ax²+bx+c=0.

step-by-step explanation:

you can see that a=1 (there is just an x²)

b = (-5 -2√7 + 2√7 - 5)/3 = -10/3

c = -2√7)/3 ) * (-5+2√7)/3) = -1/3

so your answer is 3x^2 – 10x – 1 = 0