MHR • Advanced Functions 12 Solutions 660

Chapter 7 Section 5 Question 3 Page 404
a) i) P = 1006(1.016) t
P = 1006(1.016) 100
&= 4920
The town’s population will be approximately 4920 in 100 years from 1920.
P = 1000 ! 2
t
43.5
100
P = 1000 ! 2
43.5
&= 4921
The town’s population will be approximately 4921 in 100 years from 1920.
ii)
P = 1006(1.016) t
20 000 = 1006(1.016) t
20 000
1006 = 1.016t
! 20 000$
log
"
# 1006 %
& = t log1.016
! 20 000$
log
"
# 1006 %
&
t =
log1.016
t &= 188.4
It will take approximately 188.4 years for the town’s population to reach 20 000.
P = 1000 ! 2
20 000 = 1000 ! 2
20 = 2
t
43.5
log 20 = log 2
t
43.5
t
43.5
t
43.5
log 20 =
t
43.5 log 2
t log 20
=
43.5 log 2
t =
43.5log 20
log 2
t &= 188
It will take approximately 188 years for the town’s population to reach 20 000.
b) Answers may vary. A sample solution is shown.
Quite close. The differences are due to rounding in each method.
MHR • Advanced Functions 12 Solutions 722