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

Question

x     y

 

0     0.1

1     0.2

2     0.4

3     0.8

Answer 1

Let's try to find an exponential function of the form y = A(B)^x.

 

When x = 0, y = 0.1.  So, 0.1 = A(B)⁰

 

                                            Therefore, A = 0.1

 

We have y = 0.1(B)^x

 

When x = 1,  y = 0.2.  So, 0.2 = 0.1(B).

 

                                                B = 2

 

The equation y = 0.1(2)^x is satisfied by the points (0, 0.1) and

(1, 0.2).  Checking, we see that the equation is also satisfied by the points (2, 0.4) and (3, 0.8).  

Answer 2

y= (2^x)/10 works.

 

I first recognized that pattern of 1, 2, 4, 8, etc. as being 2^x (which is exponential), and then the only difference was that it was shifted a decimal place. So I divided it all by 10. And now it works:

 

Check:

0.1 = (2⁰)/10

0.1 = (1)/10

0.1 = 0.1

 

0.8 = (2³)/10

0.8 = 8/10

0.8 = 0.8