MATH107Quiz5SOLNS.pdf - MATH 107 QUIZ 5 SOLUTIONS October,...

MATH 107 QUIZ 5 SOLUTIONS
October, 2017 Instructor: S. Sands
1. (4 pts) Which of these graphs represent a one-to-one function? Answer(s):
( no explanation required .) (There may be more than one graph that qualifies.)
D
(A)
Not a function (vertical line
crosses graph more than once),
so not a one-to-one function.
(B)
There are horizontal lines
crossing the graph more than
once.
(C)
The horizontal line y = 3
intersects the graph more
than once.
(D)
No vertical or horizontal
line crosses the graph
more than once, so the
graph represents a
function, and also is a
one-to-one function.
2. (6 pts) Students in a math class took a final exam (with a grade scale of 0 to 100) and then took equivalent
forms of the exam at monthly intervals thereafter. The average grade g after t months was found to be given by
the function
g ( t ) = 73 - 4.8 ln( t + 1), t ≥
(Note that "ln" refers to the natural log function) (explanation optional)
Using the model,
(a) What was the average grade when the students initially took the exam, when t = 0?
0.
(b) What was the average grade on the exam when taken 3 months later, to the nearest integer?
3. (4 pts) Convert to a logarithmic equation: 4
x
= 512. C
A. log
g2872
g1876=512
B. log
g3051
4=512
C. g1812g1815g1807
g2781
g2782g2778g2779=g2206 The base is 4. The value of the log is the exponent
D. log
g3051
512=4
x.

4.
(8 pts)
Solve the equation. Check all proposed solutions.
Show work in solving and in checking, and state your
final conclusion. [section 0.9, 5.3]
2
5. (8 pts)
(a)
log
g2871g2874
1= 0
because 36
0
= 1. For any base b ,
log 1
b
(b) Let
g1876=log
g2871g2874
g2869
g2869g2870g2877g2874
= 0.