Transcript powerpoint: solving_exponential eq`ns

Chapter 2 Exponents and Logarithms
2.4
MATHPOWERTM 12, WESTERN EDITION 2.4.1
Solving Exponential Equations
To solve exponential equations, you need to apply the
Laws of Exponents. One method of solving exponential
equations is based on the following property:
If ax = ay, then x = y.
That is, if 2 powers are equal and have the same bases,
then the exponents are equal.
Solve the following:
a)
92x - 3 = 27x + 4
(32)2x - 3 = (33)x + 4
34x - 6 = 33x + 12
Since both sides have the same
base, then the exponents must
be equal:
4x - 6 = 3x + 12
x = 18
b) 16 2x + 4 = 1
16 2x + 4 = 160
2x + 4 = 0
2x = -4
x = -2
2.4.2
Solving Exponential Equations
x 2
c) 9
x 2
1


  
27
(32)x + 2 = (3-3)x + 2
32x + 4 = 3-3x - 6
2x + 4 = -3x - 6
5x = - 10
x = -2
x 2
1

x  3
e) 

2

16
8 
3 x  2
1
4 x 3
2   2  2 
 (16
x2
 (24 x 4 )  2x
x2
 25 x 4
d) 2
2
2
x 1
x2
)2
x
x2 = 5x - 4
x2- 5x + 4 = 0
(x - 4)(x - 1) = 0
x - 4 = 0 or x - 1 = 0
x = 4 or x = 1
23x  6  21  24 x  12
23x  6  24x  13
-3x + 6 = 4x + 13
-7x = 7
x = -1
2.4.3
Exponential Growth
A cell doubles every 4 min. If there are 500 cells originally,
how long would it take to reach 16 000 cells?
N(t )  No  2
N(t)
No
t
d
t
d
Number of bacteria after t minutes
Number of bacteria originally
Time passed
Doubling time
N(t )  No  2
16 000  500  2
t
4
t
4
32  2
25  2
t
d
t
4
t
5
4
t = 20
Therefore, it would take
20 min for the cells to
reach 16 000.
2.4.4
Exponential Decay
The half-life of sodium 24 is 15 h. How long would it take
for 1600 mg to decay to 100 mg?
t
1  h

A(t)  Ao   
2
A(t)
Ao
t
h
Amount after a given period of time
Amount originally
Time passed
Half-life
A(t)
1 

 Ao   
2
t
1  15

100  1600 
2
t
1 1  15
  
16
2
t
h
4
t
1   1  15
2  2 
t
4
15
t = 60
It would take 60 h
to decay to 100 mg.
2.4.5
Suggested Questions:
Pages 89 and 90
1-16, 24, 30,
32, 34 a
Page 93
all
2.4.6