Section 1.5
Exponential Functions
Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved
Investment Choices
• You have $1000 to invest. Broker A offers a
$100 annual return. Broker B offers an 8%
annual compounded return. Which broker do
you prefer?
• How would your answer change if the returns
were different?
• How would your answer change if the
compounding period changed?
Applied Calculus ,4/E, Deborah HughesHallett Copyright 2010 by John Wiley and
Sons, All Rights Reserved
Population Growth
The population of Nevada from 2000 to 2006 is given in Table 1.30. To
see how the population is growing, we look at the absolute increases in
population in the third column and relative increases in the fourth
column. Is the growth linear or exponential? Why? Write a formula
that captures the trend of the data.
Table 1.30 Population of Nevada (estimated) 2000 – 2006
Year
Population
(thousands)
Change in population
(thousands)
Relative change
in population
2000
2,020
73
3.6%
2001
2,093
75
3.6%
2002
2,168
78
3.6%
2003
2,216
81
3.7%
2004
2,327
84
3.6%
2005
2,411
87
3.6%
2006
2,498
Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved
where is the population of Nevada years after 2000.
Applied Calculus ,4/E, Deborah HughesHallett Copyright 2010 by John Wiley and
Sons, All Rights Reserved
…And, a has to be positive.
Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved
Figure 1.61: Exponential growth: P = at , for a > 1
Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved
Figure 1.62: Exponential decay: P = at , for 0 < a < 1
Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved
Problem 6
A product costs $80 today. How much will the
product cost in t days if the price is reduced by
(a) $4 a day
𝑐 = 80 − 4𝑡
(b) 5% a day
𝑐 = 80 × 0.95𝑡
Applied Calculus ,4/E, Deborah Hughes-Hallett
Copyright 2010 by John Wiley and Sons, All Rights Reserved
Sales at a company are changing according to the
formula S = 1000(0.82)t , where S is sales in
thousands of dollars and t is measured in years.
Sales at this company are:
(a) Increasing by 82% per year
(b) Increasing by 82 thousand dollars per year
(c) Decreasing by 82% per year
(d) Decreasing by 82 thousand dollars per year
(e) Increasing by 18% per year
(f) Increasing by 18 thousand dollars per year
(g) Decreasing by 18% per year
(h) Decreasing by 18 thousand dollars per year
ConcepTest • Section 1.5 • Question 4
Let f(x) = abx, b > 0. Then
(a) bh
(b) h
(c) bx+h − bx
(d) a
ConcepTest • Section 1.5 • Question 10
f (x  h)
f (x)
