IN ORDER TO GET FULL CREDIT FOR EACH PROBLEM, PLEASE SHOW ALL WORK AND WRITE EVERYTHING OUT CORRECTLY USING THE LANGUAGE OF MATH.
The quiz is worth 100 points. Each problem is worth 5 points.
- Determine whether each of the following graphs represents a one-to-one
function.
(a)
No
(b)
yes
(c)
yes
(d)
No.
2. For each part below, determine if an inverse for the given f( x )
exists. If an inverse exists, then please find the inverse.
Otherwise, write “NO INVERSE”.
(a)f( x ) = 3x + 3
Inverse exists.
f-1(x) =(x-3)/3
(b)
Inverse exists.
f-1(x) =1/x
(c)f( x ) = 7
Inverse does not exist.
(d)f( x ) = 5x2 + 4x
f-1(x)=
3. In order to check to make sure we have the right inverse for a
given f( x ), we can check that and also that
. Using that idea of checking, please check to
make sure that the inverse you got in #2 (a) is the correct inverse
for f( x ) = 3x + 3.
Hence, #2(a) answer is correct.
4. The following formula can be used to convert Fahrenheit temperatures
x to Celsius temperatures T(x):
a) Find T(-13) and T(86).
b) Find T-1(x) and explain what it represents.
Interchanging T and x, we get
This can be used to convert centigrade temperatures to Fahrenheit temperatures.
5. Please choose which equation represents the following graph:
- f( x ) = -ex
- f( x ) = -ex + 1
- f( x ) = e-x + 1
- f( x ) = ex – 1
6. Please choose which equation represents the following graph:
- f( x ) = 2x - 1
- f( x ) = 2x - 1
- f( x ) = -2x - 1
- f( x ) = -2x– 1
From the graph, we see that f(3) = 0. None of the alternatives is meeting this requirement. Hence, no equation is matching with the graph.
7. Water initially at 130 degrees Fahrenheit is left in a room of temperature
70 degrees Fahrenheit to cool. After t minutes, the temperature T of the
water is given by
Find the temperature of the water 10 minutes after it is left to cool.
92.935 deg F
8. Suppose that $100,000 is invested at 4% interest, compounded
monthly. Find the amount of money in the account after 10 years.
Here A=?, P=100000,i=4/12, n = 10*12=120
Hence, A=100000*(1+4/1200)^120 =149083.27
9. Find each of the following, and round answer to the nearest 4 decimal places.
(a) e4= 54.5981
(b) e-2=0.1353
(c) log 50 = 1.6989
(d) log2 128 =7
(e) ln 50 = 3.9120
10. Find log4 50 using the change of base formula, and round answer to the
nearest 4 decimal places.
11. Students in an accounting class took a final exam and then took equivalent
forms of the exam at monthly intervals thereafter. The average score
S(t), as a percent, after t months was found to be given by the function
S(t) = 78 – 15 log(t + 1)
(a) What was the average score when the students initially took the
test?
S(0) = 78-15log(0+1) = 78-15log1 = 78
(b) What was the average score after 4 months? after 24 months?
S(4) = 78-15*log(4+1) = 67.515
S(24) = 78-15*log(24+1) = 57.03
12. Express log 2x as a sum of logarithms.
log2x = log2+logx
13. Express as a product.
ln√a = (1/2)ln(a)
14. Express as a difference of logarithms.
FOR #15 AND #16, EXPRESS IN TERMS OF SUMS AND DIFFERENCES
OF LOGARITHMS.
15
16.
FOR #17 AND #18, EXPRESS AS A SINGLE LOGARITHM, AND IF POSSIBLE, SIMPLIFY.
17. ln 44 – ln 4 =ln(44/4) = ln11
18.
FOR #19 AND #20, LET , , AND , FIND EACH OF THE FOLLOWING:
19.
= 0.845/0.301 = 2.8073
20.
= loga7+loga11 = 0.845+1.041 = 1.886