Who can do this Algebra Assignment
bigetum
algebra_assignment.rtfWA 5, p. 1
Answer all 22 exercises, and show all work in this word document. An asterisk indicates an exercise for which a graph needs to be provided, #3 and #4.
Decide whether each function as graphed or def i ned is one-to-one . (See section 4 . 1 , Example s 1 and 2 .) [ 9 points]
2
100
yx
=--
4
8
y
x
=
-
Use the definition of inverses to determine whether f and g are inverses . (See section 4 .1 , Example 3 .) [ 3 points]
()39,
fxx
=+
1
()3
3
gxx
=-
For each function as defined that is one-to-one, (a) write an equation for the inverse function in the form
1
(),
yfx
-
=
(b) graph f and f – 1 on the same axes, * and (c) give the domain and the range of f and f – 1 . If the function is not one-to-one, say so . ( S ee section 4 .1 , Example s 5– 8. ) [ 6 points]
45
yx
=-
4
,0
yx
x
=¹
Graph each function.* (S ee section 4 .2 , Example 2. ) [ 6 points]
1
()
4
x
fx
æö
=
ç÷
èø
()2
x
fx
-
=
Solve each equation. (S ee section 4 .2 , Example s 4 – 6 . ) [ 6 points]
29
34
x
æö
=
ç÷
èø
2/5
16
x
=
Future value— Find the future value and interest earned if $56,780 is invested at 5.3% compounded quarterly for 23 quarters . (S ee section 4 . 2 , Example s 7 – 9 . ) [ 3 points]
Interest rate— Find the required annual interest rate to the nearest tenth of a percent for $65,000 to grow to $65,325 if interest is compounded monthly for 6 months . (S ee section 4 . 2 , Example s 7–9 . ) [ 3 points]
If the statement is in exponential form, write it in an equivalent logarithmic form. If the statement is in logarithmic form, write it in exponential form. (S ee section 4 .3 , Example 1 . ) [ 6 points]
5
232
=
4
1
log3
64
=-
Solve each logarithmic equation. (S ee section 4 .3 , Example 2 . ) [ 6 points]
3
1
log
81
x
=
4
5
log25
x
=
Use the properties of logarithms to rewrite the expression. Simplify the result if possible. ( S ee section 4 . 3 , Example 5 . ) [ 3 points]
2
23
log
5
Given the approximations
10
log20.3010
=
and10
log30.4771
=
, find each logarithm without using a calculator . ( S ee section 4 . 3 , Example 7 . ) [ 3 points]
10
20
log
27
Find each value. If applicable, give an approximation to four decimal places . ( S ee section 4 . 4 , Example 1 . ) [ 9 points]
7
log10
log0.01
log0.0055
Earthquake intensity— On December 26, 2004, an earthquake struck the Indian Ocean with a magnitude of 9.1 on the Richter scale. The resulting tsunami killed an estimated 229,900 people in several countries. Express this reading in terms of I 0 . ( S ee section 4 . 4 , Example 4 . ) [ 3 points]
Use the change-of-base theorem to find an approximation to four decimal places for each logarithm . (See section 4 . 4 , Example 8 .) [ 3 points]
2
log9
Solve each exponential equation. E xpress irrational solutions as decimals correct to the nearest thousandth. (See section 4 . 5 , Example s 1–4 .) [ 6 points]
a.
1
6
3
x
æö
=
ç÷
èø
b.
(
)
32
51.217
x
-
+=
Solve the following logarithmic equation. Express the s olution in exact form . (See section 4 . 5 , Example s 5–9 .) [ 3 points]
ln(2)5
x
=
Investment time— Find t to t he nearest hundredth year if $1 786 becomes $2063 at 2.6%, with interest compounded monthly . Refer to the formulas for compound interest
1
tn
r
AP
n
æö
=+
ç÷
èø
andrt
APe
=
from section 4.2 [ 3 points]
Interest rate— At what interest rate, to the nearest hundredth of a percent, will $16,000 grow to 20,000 if invested for 5.25 yr and interest is compounded quarterly. Refer to the formulas for compound interest
1
tn
r
AP
n
æö
=+
ç÷
èø
andrt
APe
=
from section 4.2 [3 points]
Carbon-14 dating— A sample from a refuse deposit near the Strait of Magellan had 60% of the carbon-14 of a contemporary sample. How old was the sample? (See section 4 . 6 , Example 5 .) [ 4 points]
Dissolving a chemical— The amount of a chemical that will dissolve in a solution increases exponentially as the (Celsius) temperature t is increased according to the model
0.0095
()10.
t
Ate
=
At what temperature will 15g dissolve? [ 4 points]
Growth of an account— Russ McClelland, who is self-employed, wants to invest $60,000 in a pension plan. One investment offers 5% compounded quarterly. Another offers 4.75% compounded continuously. If Russ chooses the plan with continuous compounding, how long will it take for his $60,000 to grow to $80,000? [ 4 points]
Doubling time— If interest is compounded continuously and the interest rate is tripled, what effect will this have on the time required for an investment to double? (See section 4 . 6 , Example 2 .) [ 4 points]
