# An exponential function passes through the points #(-3, 8)# and #(0, 1)#. What is the equation of the function?

##### 1 Answer

The function has equation

#### Explanation:

It may look like you only have

Every exponential function has its y-intercept at

We conclude the equation can be written in the form

#y = ab^x#

We can write a system of equations in two variables to solve for parameters

#{(8 = ab^-3), (1 = ab^0):}#

We can see by inspection, using the property

We can now readily solve for

#8 = 1(b^-3)#

#8 = b^-3#

#2^3 = b^-3#

#2^3 = 1/b^3#

#b^3 = 1/2^3#

#(b^(3))^(1/3) = (1/2^3)^(1/3)#

#b = 1/2#

The function therefore has equation

**Practice Exercises**

- Find the equation of the exponential function given:

a) It passes through the points

b) The following graph:

**Solutions**

1a)

1b)

Hopefully this helps!