Unit 7
MHF 4U1
Lesson 1– Exponent Laws and Problems
Recall the following exponent laws:
Multiplication:
a m  a n  a m n
Division:
am
 a mn
n
a
Powers:
(a m ) n  a mn
Power of a Product: (ab)
m
Power of a Quotient:
 a mb m
m
am
a
   m
b
b
Negative and Zero Integral Exponents
x n 
x0  1
1
xn
Rational Exponents
1
n
x  x
n
and
n N
x  0 if n is even
x

1
n
1
n
x
and
n  N, x  0
x  0 if n is even.
m
n
x  n x m  (n x ) m
x0
n N
if n is even.
Examples: Simplify then evaluate the following expressions. Express answers in rational
form.
a) 23 (25 ) 2
b)
52
56 (52 ) 1
Unit 7
 31 
c)  1 
2 
f) 25
i)
MHF 4U1
2
51  2 2
d) 1
5  2 2
3
2
1
 
 23
 3  2 2 




g) (8)
6
2
3
 1
h)   
 8
 1
j)  xy 2 




3
x y 
2
1
2

2
3
Unit 7
MHF 4U1
Exponential growth and decay occur when quantities increase or decrease
respectively at a rate proportional to the quantity present. This growth or decay occurs
in savings accounts, the size of populations, and the quantity of decay that occurs in
radioactive chemicals. All situations of this type can be expressed using the exponential
function.
Problems involving growth and decay can be solved using exponential functions in the
x
form y  ca where:
c is the original amount
x is time (the exponent)
a is the growth factor (the base)
Examples
1. Doubling Period
A very convenient measure of population growth is a doubling period. The population
of the world was 6 billion in 1999. This population is growing exponentially and
doubles every 35 years.
a) Estimate the world population in 2050, to the nearest half billion.
b) When will the population be 24 billion?
2. Rate of Increase
The population of Nerdville was 24,000 in 1980 and 29,000 in 1990.
a) Determine an expression for the population at the time t years after 1980.
Unit 7
c)
MHF 4U1
Use this expression to estimate the population of the town in 2020.
Rate of Decrease
Each year a car depreciates by 30%.
value after 5 years.
If a car was bought new for $10 000, find its