Question

What type of function is represented by the table of values below?

Answer 1

Answer:

Step-by-step explanation:

This is exponential. I'll show you how I found it. After many attempts at other types of functions, I realized the points were either forming a quadratic or an exponential. Definitely not a line.

the standard form of an exponential function is

$y=a(b)^x$ so we sub in coordinates from the table to determine what the equation is and then test it on another set of points to see if it works. Using the first coordinate of (1, 2):

$2=a(b)^1$ so

$a=\frac{2}{b}$ . The next  coordinate is (2, 4), so:

$4=\frac{2}{b}(b)^2$ which simplifies down to

4 = 2b so

b = 2. Now we plug in 2 for b and solve for a:

a = 2/2 which is 1. So the equation, if this is exponential, is

$y=1(2)^x$ Let's test the next point in line and see if it works, (3, 8):

$8?=?1(2)^3$ and yes, 8 is equal to 2 cubed. And the next point says that 16 should equal 2 to the 4th, and it does, as well. So this is exponential...growth to be specific.