Exponential Growth and Decay Worksheet
1.
t
4
A bacteria culture grows according to the formula: N = 12000 2 , where t is in
hours. How many bacteria are present
(a)
(b)
(c)
(d)
at the beginning of the experiment? (answer 12 000)
after 12 hours? (answer 9
Factorials Worksheet
1. Can a factorial be defined for a negative number?
2. Express in factorial form:
a)
b)
c)
d)
6x5x4x3x2x1
8x7x6x5x4x3x2x1
3x2x1
9x8x7x6x5x4x3x2x1
3. Match each expression on the left with an equivalent expression on the right.
Letter
Organized Counting Worksheet
1. Construct a tree diagram to illustrate the possible contents of a sandwich made from
white or brown bread; ham, chicken or beef; and mustard or mayonnaise. How many
different sandwiches are possible?
2. In how many ways can
Factorials
Example 1
a) 7 ! =
b) 4 ! =
c) 23! =
d) n ! =
Example 2
Evaluate using a calculator.
a) 4!
=
b) 5!
=
c) 7!
=
Example 3
Evaluate using a calculator.
8!
a) 6!
175!
b) 171!
=
=
Part a) was possible on the calculator but b) wasnt. Error 2 indicates
Organized Counting
Example 1
A company makes gloves that are black, blue, burgundy or grey. Each of the colours comes in
small. medium and large size. How many different types of gloves does the company make?
(Use a tree diagram)
Example 2
A restaurant ha
Exponential Growth and Decay
1.
An influenza bug has infected 8 students. Every day the number of students infected with
the bug doubles.
(a)
Complete the table of values below.
Number of Days
Number of
People Infected
How calculated?
At start, time = 0
(
Review of Exponent Laws
When multiplying powers with the same base, keep the base the same and add the
exponents.
a7 a5 =
43 4 2 =
When dividing powers with the same base, keep the base the same and subtract the
exponents.
512
=
53
a12 a 7 =
When evaluati
Solving Exponential Equations
Basic Rule: Get the same bases on either side of the equation. Set the exponents equal
and solve.
Example 1 Solve
a) 3x = 27
b)
6561 = 9t
c)
( 4 )
m
= 4096
x
d) ( 5 ) = 125
3x = 33
Therefore
x=3
Example 2 Solve
a) 4 x +3 = 10
Venn Diagrams
Given the sets A = cfw_1,2,3 , B= cfw_ and C=cfw_2,4,6,8
Objects in a set are called elements or members
For the set A the elements are _
For the set C the elements are _
use cfw_ to denote a set
the curly brackets indicate a set
Order in
Graphs of Exponential Functions
1.
Complete the table of values at the side to graph each of the following
x
4
3
2
1
0
1
2
3
4
y = 2x
y = 3x
y = 5x
2.
Complete the table of values at the side to graph each of the following
x
4
3
2
1
0
1
2
3
4
1
y=
2
x
1
Skills Review: Algebra and Exponent Laws
1. Simplify each of the following. (Collect like terms)
a)
3c + 8c
b)
7w 4w
c)
2 x + 3x + 4 x
d)
4 y + 3y 5y
e)
7 x 2 + 3x 2
f)
7t 9t
g)
3c 2 2c + 6c 2c 2
h)
4 x + 11x
i)
5x 2x + x
j)
5 y2 7 y2 + 2 y2
k)
3 x 4 y +