Question

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

Answer 1

Answer:

Step-by-step explanation:

If this is an exponential function, it is of the form

$y=a(b)^x$  where x and y are coordinates from your table, a is the intial value, and b is the growth/decay rate.  To find out what the equation is that represents this data, choose 2 points and solve first for a and then for b.  Just a hint:  If at all possible, choose the coordinate that gives you an x of 0.  You'll see why in a minute.  

I chose the first 2 points from your table: (0, .2) and (1, .8).  Solving first for a:

$.2=a(b)^0$  The reason to choose the x of 0 as one of your points is because anything raised to the power of 0 is 1.  So our equation then becomes:

$.2=a(1)$ so

a = .2   Easy enough.  

Now use that value along with the other coordinate to solve for b:

$.8=.2(b)^1$  b to the first is just b, so,

.8 = .2b

Divide both sides by .2 and you'll get that

b = 4

The equation, then, is

$y=.2(4)^x$ which is growth, since the value for b is greater than 1.