MHR • Advanced Functions 12 Solutions 660

e) How many bacteria will there be after two weeks?
Solution:
200
y =
1+181e !0.953x
200
y =
1+181e !0.953(14)
y &= 199.9
There will be about 199 900 bacteria.
After how many days did the bacteria population reach 100 000?
Solution:
200
100 =
1+181e !0.953x
1+181e !0.953x = 200
100
e !0.953x = 2 !1
181
log e !0.953x = log 1
181
!0.953x log e = log 1
181
log 1
x = !
181
0.953log e
x &= 5.45
The population reached 100 000 just before 5.5 days.
Chapter 7 Section 5 Question 14 Page 407
Answers may vary. A sample solution is shown.
The data is constantly curving, so a piecewise linear would not be the best option.
If there were more data about the end behaviour, it might be possible to approximate the data
using two almost horizontal function (especially since the data is levelling off towards y = 200),
with a steep linear function in the middle.
MHR • Advanced Functions 12 Solutions 731