Intermediate Algebra – Student Workbook – Second Edition 2013

Lesson 3a – Introduction to Exponential Functions
Mini-Lesson
e) Let’s see if we can understand WHY option B grows so much faster. Let’s focus just on
options A and B. Take a look at the data tables given for each function. Just the later parts of the
initial table are provided.
t =
time in # of
days
A(t) = 1000t + 1000
A(t)=
$ in account after t days
20 21,000
21 22,000
22 23,000
23 24,000
24 25,000
25 26,000
26 27,000
27 28,000
28 29,000
29 30,000
30 31,000
31 32,000
t =
time in # of
days
B(t) = .01(2) t
B(t) =
$ in account after t
days
20 10,485.76
21 20,971.52
22 41,943.04
23 83,886.08
24 167,772.16
25 335,544.32
26 671,088.64
27 1,342,177.28
28 2,684,354.56
29 5,368,709.12
30 10,737,418.24
31 21,474,836.48
As t increases from day 20 to 21, describe how the outputs change for each function:
A(t):
B(t):
As t increases from day 23 to 24, describe how the outputs change for each function:
A(t):
B(t):
So, in general, we can say as the inputs increase from one day to the next, then the outputs for
each function:
A(t):
B(t):
In other words, A(t) grows ______________ and B(t) grows ______________. We have just
identified the primary difference between LINEAR FUNCTIONS and EXPONENTIAL
FUNCTIONS.
Exponential Functions vs. Linear Functions
The outputs for Linear Functions change by ADDITION and the outputs for
Exponential Functions change by MULTIPLICATION.
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