What is the function given the table below.

Question

X           Y

 

-4          243/16

-3           81/8

-2           27/4

-1             9/2

 0               3

Answer 1

There are a few ways you can do this, but I will try to make it simple. Since you are told that this is an exponential function, it means that every value in the table will be a constant times the value just before it.

 

For this table, the constant is b = 2/3.

 

Check this:

 

243/16 · b = 81/8   OK

81/8 · b = 27/4   OK

27/4 · b = 9/2   OK

9/2 · b = 3  OK

 

This means that the exponential function will take the form y = 3b^x = 3(2/3)^x .

 

The 3 is the y-intercept (value when x = 0). You can check this by plugging in the same values for x as in the table, calculating the y values, and verifying they are the same.

 

Example,

 

x = -4 ⇒ y = 3(2/3)^-4 = 3(3/2)⁴ = 3(3⁴/2⁴) = 3(81/16) = 243/16.

 

It checks out!

Answer 2

 

 

 

 

                          2^x_*3^1-x