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Notes #3-___
Date:______
8-8 Exponential Growth and Decay (437)
W.1 Evaluate each exponential function for the given
domain.
x
a) y  5 {2,3,4}
b) g(x)  2 3x {-2,0,3}
W.2
Find the next term of each sequence.
a) 2.5, 2, 5, 10…
b) -8, 4, -2, 1…
W.3
Simplify each expression.
2a 3b 4 a 5
a)
4b 2

1
b) 3mn
m
3
2
Exponential Growth:
y  a bx
a > 0, starting amount
b > 1, growth factor
Ex. 1 In 1998, a certain town had a population of about
10,000 people. Since 1998, the population has
increased about 2% a year. Write an equation to model
the population increase and approximate the population
in 2000.
a = 10,000
b = 100% + 2% = 1.02
y 10,000 1.02 x
x = 2000 – 1998 = 2
y 10,000 1.022 = 10,404
annually
1x/yr
semi-annual 2x/yr
quarterly
4x/yr
monthly
12x/yr
Ex.2
A savings certificate of $1000 pays 6.5% annual
interest compounded yearly. What is the balance
when the certificate matures after 5 years?
Ex.3 Suppose the savings certificate in Example 2 paid
interest compounded quarterly instead of annually.
Write the equation representing the balance after 5
years.
Exponential Decay:
y  a bx
a > 0, starting amount
0 < b < 1, decay factor
Ex.4 Technetium-99 has a half-life of 6 hours. Suppose a lab
has 80 mg of technetium-99. How much technetium-99
is left after 16 hours?
a = 80
b = 100% - 50% = .5
y  80 0.5x
x  24  6  4
y  80 0.54  5mg
Ex.5 From 1983 to 1997, the ratio of students per computer
at the school has dropped by about 6.8% per year. If
there were 103 students per computer in 1983, what
was the number of students per computer in 1997?
a = 103
b = 100% - 6.8% = .932
y 103 .932 x
x = 1997 – 1983 = 2
y 103 .93214 ≈ 38 students
Ex.6 You bought a computer for $1800. The value of the
computer will be less each year because of
depreciation. The computer depreciates at the rate of
29% per year.
a) Write an exponential decay model for this situation.
b) Estimate the value of the computer in two years.
Ex.7 Classify as growth or decay. Identify the growth or
decay factor and the percent of increase or decrease.
a) y40 0.75t
Summary:
6
b) y40  
5
t
Notes #3-___
Date:______
10-3 Finding and Estimating Square Roots (525)
W.1 Evaluate the expression without using a calculator.
Write the result in decimal form.
12
a) (9  10 )  (6  10 )
3
1.8  10 2
b)
2.4  10 7
W.2 The function y10 1.08 x models the cost of annual
tuition (in thousands of dollars) at a local college x
years after 1997.
a) What is the annual percent increase?
b) How much was tuition in 1997?
c) How much will the tuition be the year you graduate
from high school? (write the function)
*
If b2 = a, then b is a square root of a.
*
The convention is to use
*
symbol
names the principal square root and names the negative square root. The symbol ± indicates
both.
The number inside is the radicand .
*
Numbers with rational square roots are perfect squares.
The 2 is called
the index.
instead of 2
. The
Ex.1 Simplify each expression.
9
a) 25
b) 
25
d)
*The
49
e)
c)
1
16

f)
64
0
negative number results in an imaginary number.
Rational number:
can be expressed as
a ratio of two
integers
*Some square roots are rational numbers and some are
irrational numbers.
(integers, fractions,
ending/repeating
decimals)
Ex.2 Tell whether each is rational or irrational.
1
a)  144
b) 
c)  6.25
5
1
9
d)
List the first 12
perfect square
natural numbers.
e)
f) 
7
What if we do not have a perfect square? We can estimate a
square root by using the two nearest perfect squares.
Ex.3 What two whole numbers is the root closest to?
a)
2 ≈ 1.41
b)
3 ≈ 1.73
c)
14 ≈
d)
53 ≈
Ex.4 Using a calculator, approximate the square root to the
nearest hundredth.
a) 17.81
b) 28.34
Summary:
Ex.5 The formula d x 2 (3x)2 gives the length of the
diagonal of a rectangular field that has a length three times its
width x. Find the length of the diagonal if x = 8 ft.