1. Examine the functions P, Q, and R
in Section 3.4 Example 1 written in the form P =aekt.
For the function P, what is the value of
k? _____ Is P increasing or decreasing? _____________
For the function Q, what is the value of
k? _____ Is Q increasing or decreasing? _____________
For the function R, what is the value of
k? _____ Is R increasing or decreasing? _____________
2. Each of the functions P, Q, and R in
Section 3.4 Example 1 can be written in the form a(b)t
for some numbers a and b. If so,
what would be the value of a? _______
3. Each of the functions P, Q, and R in
Section 3.4 Example 1 can be written in the form a(b)t
for some numbers a and b.
Give the value of b for P =5e0.3t
(round to two decimal places)_________
Give the value of b for Q =5e0.2t
(round to two decimal places)_________
Give the value of b for R =5e−0.2t
(round to two decimal places)_________
4. Suppose each of the functions P, Q, and R
in Section 3.4 Example 1 represented populations of
different countries (in millions), where t
is given in years.
For P =5e0.3t
the population grows at an annual rate of _____% per year
and at
a continuous rate of ____% per year.
For Q =5e0.2t
the population grows at an annual rate of _____% per year
and at
a continuous rate of ____% per year.
For R =5e−0.2t
the population decreases at an annual rate of _____% per year
and at
a continuous rate of ____% per year.
5. Suppose Account A pays 52% interest once per year. (OK, use your
imagination.)
Account B pays 1% interest every week. (Note there are 52 weeks in a year.)
Without a calculator, decide which account is better after 1 year.
o Account A
o Account B
o Both the same.