# How do you find an exponential function given the points are (-1,8) and (1,2)?

##### 1 Answer

#### Explanation:

An exponential function is in the general form

#y=a(b)^x#

We know the points

#8=a(b^-1)=a/b#

#2=a(b^1)=ab#

Multiply both sides of the first equation by

#8b=a#

Plug this into the second equation and solve for

#2=(8b)b#

#2=8b^2#

#b^2=1/4#

#b=+-1/2#

Two equations seem to be possible here. Plug both values of

**If** **:**

#2=a(1/2)#

#a=4#

Giving us the equation:

**If** **:**

#2=a(-1/2)#

#a=-4#

Giving us the equation:

**However!** In an exponential function,

The only valid function is

#color(green)(y=4(1/2)^x#