MCV4U1-UNIT FIVE-LESSON THREE
Lesson 3: Optimization Problems Involving Exponential Functions
1.
An ant population, P t  of a rare Brazilian ant is given by P t   1000e 0.3t ,
where t is the time in days. Find the rate of change of population when t=2
and when t=5.
2.

 activity is needed and is socially desirable,
When a new
such as waste
recycling, its growth is rapid at first and then levels off. Suppose the sale of
waste-recycling plants is given by St   100  90e 0.3t , where t is the time in
years and St  represents sales in year t. Find the rate of change of sales
when t=1 and when t=10.
3.
t

20
N

t


2000[30

te
]. Find
The
number
N
of
bacteria
in
a
culture
at
time
t
is

the largest number of bacteria in the culture during the interval 0  t  50,
where t is measured in hours.
4.
The net monthly profit from the sale of acertain product is given (in dollars)
 number of items
by the formula P x   10 6 1  x  1e 0.001x , where x is the
sold.
a)
Find the number of items that yield the maximum profit. Assume that at
 items can be produced per month.
most 2000
b)
Repeat part a) assuming that at most 500 items can be produced per month.


hw: P.245-247 #4, 5, 6, 8, 12(use graphmatica), 13