MHR • Advanced Functions 12 Solutions 660

Chapter 7 Review Question 16 Page 408
!
a) t = 5 log0.2 $
"
# log0.5%
&
&= 11.6
It takes approximately 11.6 h for the caffeine to drop to 20%.
!
b) 3 = 5 log P $
"
# log0.5%
&
3
5 = log P
log0.5
3
log0.5 = log P
5
3
log0.5 5
= log P
3
P = 0.55
P &= 0.66
Approximately 66% of the caffeine will remain in the body at noon.
Chapter 7 Review Question 17 Page 409
a) P = 500, i = 0.066 , n = 2t
2
= 0.033
A = P(1 + i) n
= 500(1+ 0.033) 2t
= 500(1.033) 2t
b) A = 500(1.033) 10
&= 691.79
The investment is worth $691.79 after 5 years.
c) 2 = (1.033) 2t
log 2 = 2t log1.033
2t =
t =
log 2
log1.033
log 2
2log1.033
t &= 10.67
It will take approximately 10.67 years for the investment to double.
MHR • Advanced Functions 12 Solutions 741