SA
=
6
s
2
SA
=
6(
4
)
2
SA
=
6(16)
SA
=
96
The surface area of the cube is 96 cm
2
.
b)
The diagram models the Pythagorean relationship. The relationship
between the areas of the squares on the sides of a right triangle is
represented by the formula
c
2
=
a
2
+
b
2
, where
a
and
b
are the legs
of the triangle and
c
is the hypotenuse.
c
2
=
a
2
+
b
2
c
2
=
5
2
+
12
2
c
2
=
25
+
144
c
2
=
169
The area of the square attached to the hypotenuse is 169 cm
2
.
3.4 Using Exponents to Solve Problems
•
MHR
115
Use a formula to solve each problem.
a)
A right triangle has two shorter sides that
measure 8 cm and 15 cm. What is the area
of a square attached to the hypotenuse of
the right triangle?
b)
What is the surface area of a cube with an edge
length of 3 m?
Show You Know
c)
Method 1: Calculate in Stages
The formula for the area of a square is
A
=
s
2
, where
s
is the side length
of the square.
A
=
s
2
A
=
20
2
A
=
400
The area of the square is 400 cm
2
.
The formula for the area of a circle is
A
=
π
r
2
, where
r
is the radius of
the circle.
The diameter of the circle is 20 cm. Therefore, the radius is 10 cm.
A
=
π
r
2
A
=
π
(
10
)
2
A
=
π
(100)
A
≈
314 …
The area of the circle is approximately 314 cm
2
.
Calculate the area of the shaded region. You can subtract the area of
the circle from the area of the square.
400

314
=
86
The area of the shaded region is about 86 cm
2
.
Method 2: Evaluate One Expression
Calculate the area of the shaded region. You can subtract the area of
the circle from the area of the square.
A
=
s
2

π
r
2
A
=
20
2

π
(
10
)
2
A
=
400

π
(100)
A
≈
400

314
A
≈
86
The area of the shaded region is about 86 cm
2
.
15 cm
8 cm
3 m
116
MHR
•
Chapter 3
Example 2:
Develop a Formula to Solve a Problem
A dish holds 100 bacteria. It is known that the bacteria
double in number every hour. How many bacteria
will be present after each number of hours?
a)
1
b)
5
c)
n
Solution
a)
After 1 h, the bacteria population doubles.
100
×
2
=
200
After 1 h, there will be 200 bacteria.
b)
In a period of 5 h, the bacteria population
doubles five times.
100
×
2
×
2
×
2
×
2
×
2
=
100(2
5
)
=
100(32)
=
3200
After 5 h, there will be 3200 bacteria.
c)
After
n
hours, the bacteria population doubles
n
times.
Number of bacteria
=
100(2
n
)
After
n
hours, there will be 100(2
n
) bacteria.
A type of bacterium is known to triple every hour. There are 50 bacteria
to start with. How many will there be after each number of hours?
a)
3
b)
5
c)
t
Show You Know
Use a Variable
Strategies
Key Ideas
•
Powers are found in many formulas. When repeated
multiplication is present in a formula, it is represented as a
power. The use of powers keeps the formula as short as possible.
•
Many patterns that involve repeated multiplication can be
modelled with expressions that contain powers.
s
s
s
Volume of a cube
=
s
3
3.4 Using Exponents to Solve Problems
•
MHR
117
Check Your Understanding
Communicate the Ideas
1.
The surface area,
SA
, of a sphere can be calculated using the formula
SA
=
4
×
π
×
r
×
r
, where
r
is the radius. Rewrite the formula using
powers and no multiplication signs. Identify the coefficient, variable,
and exponent in your formula.
You've reached the end of your free preview.
Want to read all 32 pages?
 Fall '14
 Exponential Function, Power, Alice in Wonderland, Orders of magnitude, Exponentiation, Power of two