Intermediate Algebra – Student Workbook – Second Edition 2013

Lesson 3a – Introduction to Exponential Functions
Mini-Lesson
When working with EXPONENTIAL FUNCTIONS, as with LINEAR FUNCTIONS, there are
two main questions we will ask and solve as follows:
Given a particular INPUT value, what is the corresponding OUTPUT value?
Given a particular OUTPUT value, what is the corresponding INPUT value?
Problem 9 MEDIA EXAMPLE – GIVEN INPUT FIND OUTPUT
Use the functions f(x) = 125(1.25) x and g(x) = 125(0.75) x to respond to the questions below.
a) Find f(x) when x = 2. b) Find g(x) when x = 2.
c) Find f(x) when x = -4. d) Find g(x) when x = -4.
Problem 10
WORKED EXAMPLE – GIVEN OUTPUT FIND INPUT
Given f(x) = 125(1.25) x find x when f(x) = 300. Round your respond to two decimal places.
To do this, we need to SOLVE the equation 125(1.25) x = 300 using a process called the
INTERSECTION METHOD on our graphing calculators.
To solve 125(1.25) x = 300
Press Y= then enter Y1 = 125(1.25) x and Y2 = 300
Note: You could also let Y1 = 300 and Y2=125(1.25) x
Press WINDOW then enter the values at right.
Try to determine why these values were selected. You must
see the intersection in your window. Other entries will
work. If you graph and do not see both graphs AND where
they intersect, you must pick new WINDOW values until
you do.
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Scottsdale Community College Page 106 Intermediate Algebra