MHR • Advanced Functions 12 Solutions 660

Chapter 7 Review Question 7 Page 408
a) (4 x ) 2 – 4 x – 20 = 0
a = 1, b = –1, c = –20
4 x = !(!1) ± (!1)2 ! 4(1)(!20)
2(1)
4 x =
1± 81
2
4 x = 1± 9
2
4 x = 5 or 4 x = !4 extraneous root since the base is negative
x log 4 = log5
x = log5
log 4
b) 2 x (2 x ) +12(2 ! x )(2 x ) ! 7(2 x ) = 0
( 2 ) x 2 ! 7 2 x
( ) +12 = 0
(2 x ! 4)(2 x ! 3) = 0
2 x = 4 or 2 x = 3
2 x = 2 2 x log 2 = log3
x = 2
x = log3
log 2
Chapter 7 Review Question 8 Page 408
!
a) 1516 = 2000 1 $
"
# 2%
&
0.758 = 1 2
1
h
log0.758 = 1 h log 1 2
1
h = log0.758
log 1 2
h =
log 1 2
log0.758
h &= 2.5
The half-life is approximately 2.5 years.
1
h
t
2.5
b) 0.10 &= 1 2
log0.10 &=
t
2.5 log 1 2
t log0.10
&=
2.5
log 1 2
t &= 2.5log0.10
t &= 8.3
log 1 2
It will take approximately 8.3 years to
depreciate to 10% of its purchase price.
MHR • Advanced Functions 12 Solutions 738