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!