Week 4 of m151
(§ 2, Mr. Lane)
13–17 February 2017
Math Learning Center (in Math 011) has tutors:
9am–4pm on Monday–Thursday and 9am–1pm on Friday
math@Mansfield (Library) has tutors:
6:30pm – 9:00pm on Sunday–Thursday
- Monday [d11] (13 February 2017)
WeBWorK:
RQ-4-2 closes at 10 am,
day-09 closes at 11 pm
- Study section 4.2
(Comparing Exponential and Linear Functions).
- Example 3 compares one exponential model for population growth
with three linear models for growth of the food supply.
After studying the text's version of Example 3,
- examine the effect of decreasing the rate
of population growth
- examine the effect of improving the food supply
- Suppose L(x) is a linear function and E(x) is a related
exponential function. Consider several ways to compare them.
- y_{1} = L(x) and
y_{2} = E(x)
are plotted together; use Trace and
ZoomBox to estimate intersections.
- y_{3} = L(x) − E(x)
= y_{1} − y_{2}
is plotted; locate zeros of difference
- y_{4} = L(x) / E(x)
= y_{1} / y_{2}
is plotted; compare ratio to 1 and 0
- Exponential growth always outpaces
Linear Growth in the Long Run.
- Work on these items at end of §4.2:
s3, s5, s9;
3, 5, 8, 13;
31, 32, 33, 44
- Tuesday [d12]
WeBWorK:
RQ-4-3 closes at 10 am,
day-10 closes at 11 pm
- Study section 4.3 (Graphs of Exponential Functions)
through Example 3. Notice places where a horizontal asymptote
provides a graphical summary of long run behavior.
- Work on these items at end of §4.3:
2–3, 7–8, 9, 13, 17;
23, 25–28, 35, 37–38, 41
- Study section 4.4 (Applications to Compound Interest)
through Example 2. The discussion of Nominal versus Effective
rates (page 165) is important.
- Work on these items at end of §4.4:
3, 6, 9, 13
- Anticipate a quiz on Tuesday or Wednesday.
- Wednesday [d13]
WeBWorK:
RQ-4-4 closes at 10 am,
day-11 closes at 11 pm
- Adapt Example 4.4:1 (pages 165–6) by considering
annual compounding of twelve-percent interest
for a three-year period starting with initial deposit of $1000.
- Compute a table showing account balance at six-month intervals
for that three-year period.
- Sketch a graph of account balance as a function of time t.
- Consider how your table and graph should change if interest were
compounded quarterly (i.e., at three-month intervals).
- Study Example 3 in section 4.4; then work on problems
15, 16, 17, 19, 21, 22 in §4.4.
- Study section 4.5 (The Number e).
This special base of an exponential function is important for modeling
change occurring in continuous time, e.g., radioactive decay.
- continuous growth rate is mentioned on page 168
- a discussion of the difference between annual rate
and continuous rate is on page 170.
- Work on these items at end of §4.5:
s1–s4, s9–s11;
1–7;
15, 17, 19, 25, 47
- Friday [d14] (17 Feb 2017)
WeBWorK:
RQ-4-5 closes at 10 am,
day-12 closes Saturday at 11 pm
- Write-up solutions of these four problems —
show your work and interpret your results. Hand-in your written
homework at the start of Friday's class.
section |
4.1 |
4.2 |
4.3 |
4.4 |
problems |
34 |
42 |
42 |
20 |
- Our study of section 5.1 (Logarithms and Their Properties)
will involve two related logarithm functions.
- Study §5.1 through Example 5 (page 190) — this
involves the base-ten logarithm, log.
- Read Misconceptions
(bottom of page 191 and top half of page 192).
Demonstrate each "not the same" statement by
finding a numerical example.
- Study bottom half of page 192 which discusses how to rewrite
the logarithm of a product.
- Work on these items at end of §5.1:
s1, s2, s4, s8, s9;
1, 5, 9, 13 & 15, 29;
35, 39–44, 45, 53, 78
© Richard B Lane
Last modified: 16 March 2017, Thursday 19:10