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Math 4 – Chapter 3 REVIEW
Period
1. The table at the right shows the numbers y (in thousands) of pilots and copilots in the U.S. scheduled airline
industry from 1994 to 2000. (Source: Air Transport Association of America)
(a) Use the regression feature of your TI-84 to find a quadratic model, an
exponential model, and power model for the data. Let x represent the year, with
x  4 corresponding to 1994. (Round all variables to 3 decimal places.)
(b) Determine which model best fits the data and explain why you chose that
model.
(c) Use the model you chose in part (b) to predict the number of pilots and
copilots in 2006.
(d) What is the residual value for the year 1998 in the exponential model?
(e) For the residual value in part (d), is the model an overestimate or
underestimate?
(a) Quadratic Model
ŷ 
r2 
Exponential Model
(c)
(d)
(e)
r
sum  L Resid 2  
r
sum  L Resid 2  
ŷ 
r2 
(b)
sum  L Resid 2  
ŷ 
r2 
Power Model
r
Year
1994
1995
1996
1997
1998
1999
2000
Number of
pilots and
copilots, y
52.9
55.4
57.6
60.4
64.1
67.2
72.6
2. Find the domain, vertical asymptote, and the x-intercept (exact value) of the logarithmic function
f  x   log2  x 1  6 , and sketch and completely label its graph.
Domain:
Vertical Asymptote:
x-intercept:
 x 2  16 
3. Use the properties of logarithms to expand log5 
 , where x  4.
4
 x 
 xy 5 
4. Use the properties of logarithms to expand ln 
.
 z
1
5. Write 2 log x  log  x  5  as a logarithm of a single quantity.
2
1
6. Write ln 5  ln  2  x 2   ln 2 x as a logarithm of a single quantity.
3
7. Evaluate the logarithm using the change-of-base formula.
log5 21 
8. Solve the logarithm equation algebraically. Round your result to three decimal places.
ln x  ln5  4
9. Solve the logarithm equation algebraically. Round your result to three decimal places.
log  x  2  log x  log  x  5
10. Solve the exponential equation algebraically. Round your result to three decimal places.
14e
3 x  2
 25
11. Solve the exponential equation algebraically. Round your result to three decimal places.
e2 x  6e x  8  0
12. The population of rabbits at Mar Vista after t months is modeled by the function P  t  
a. What is the population at t  0?
a.
b. When will the population reach 1500?
b.
c. What is the significance of the constant 3886?
3886
,
1  57e 0.08t