4.1 Homework-Diana Marquez
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4.1 Homework-Diana Marquez
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2.
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4.
5.
Student: Diana Marquez
Date: 12/22/23
Instructor: Karen Scott
Course: Math 1314 TD017 Fall 2023
Assignment: 4.1 Homework
Approximate each number using a calculator.
9
7
(Round to three decimal places.)
9
7
334.725
Approximate the number using a calculator. − 0.59
(Round to three decimal places.)
− 0.59
0.554
Graph the given function by making a table of coordinates.
f(x) = 5
x
Complete the table of coordinates.
x
2
−
1
−
0
1
2
y
1
25
1
5
1
5
25
(Type integers or fractions. Simplify your answers.)
Choose the correct graph below.
A.
-1
1 2 3 4 5 6
-2
-1
1
2
x
y
B.
-3 -2 -1
1 2 3
5
10
15
20
25
30
x
y
C.
-3 -2 -1
1 2
5
10
15
20
25
30
y
Graph the following function by making a table of coordinates. If applicable, use a graphing utility to confirm your hand-drawn graph.
g(x) =
8
5
x
Choose the correct graph below.
A.
-3
3
-10
10
x
y
B.
-3
3
-10
10
x
y
C.
-3
-10
10
y
Graph the given function by making a table of coordinates.
f(x) =
1
2
x
Complete the table of coordinates.
x
2
−
1
−
0
1
2
y
4
2
1
1
2
1
4
(Type integers or fractions. Simplify your answers.)
Choose the correct graph below.
A.
1
2
-2
-1
1
2
x
y
B.
-3 -2 -1
1 2 3
2
x
y
C.
-3
2
4
y
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4.1 Homework-Diana Marquez
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6.
7.
8.
The graph of an exponential function is given. Select the function for each graph from the given options.
Drag each function given above into the area below the appropriate graph, depending on which function is represented by which graph.
19.
-3
3
-10
2
x
y
20.
-3
3
-2
10
x
y
21.
-3
3
-10
2
x
y
22.
-3
3
-2
10
x
y
23.
-3
3
-2
10
x
y
24.
-3
3
-2
10
x
y
YOU ANSWERED:
Use the compound interest formulas and to solve the problem given. Round answers to the nearest cent.
A = P
1 +
r
n
nt
A = P
rt
Find the accumulated value of an investment of for years at an interest rate of if the money is a.
compounded semiannually; b.
compounded quarterly; c.
compounded monthly; d.
compounded continuously.
$20,000
4
4.5%
a. What is the accumulated value if the money is compounded semiannually?
$
23,896.62
(Round your answer to the nearest cent. Do not include the $ symbol in your answer.)
b.
What is the accumulated value if the money is compounded quarterly?
$
23,920.30
(Round your answer to the nearest cent. Do not include the $ symbol in your answer.)
c.
What is the accumulated value if the money is compounded monthly?
$
23,936.29
(Round your answer to the nearest cent. Do not include the $ symbol in your answer.)
d.
What is the accumulated value if the money is compounded continuously?
$
23,944.35
(Round your answer to the nearest cent. Do not include the $ symbol in your answer.)
Suppose you have to invest. Which of the two rates would yield the larger amount in : % compounded or compounded continuously?
$10,000
1 year
10
daily
9.94%
Which of the two rates would yield the larger amount in ?
1 year
10% compounded daily
9.94% compounded continuously
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4.1 Homework-Diana Marquez
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9.
10.
Use a calculator with a y
x
key or a key to solve the following.
The exponential function f(x)
models the population of a country, f(x), in millions, x years after . Complete parts (a)
(e).
= 550(1.032)
x
1972
−
a.
Substitute 0 for x and, without using a calculator, find the country's population in 1972.
The country's population in was million.
1972
550
b.
Substitute for x and use your calculator to find the country's population, to the nearest million, in the year as modeled by this function.
22
1994
The country's population in was million.
1994
1100
c.
Find the country's population, to the nearest million, in the year as predicted by this function.
2016
The country's population in will be million.
2016
2199
d.
Find the country's population, to the nearest million, in the year as predicted by this function.
2038
The country's population in will be million.
2038
4398
e.
What appears to be happening to the country's population every years?
22
A.
It appears that the population is decreasing by a factor of every years.
1
2
22
B.
It appears that the population is growing by a factor of 2 every years.
22
C.
It appears that the population is growing by a factor of 3 every years.
22
D.
There does not appear to be a pattern.
YOU ANSWERED:
910
3400
The bar graph shows the percentage of country A high school seniors who applied to more than three colleges for selected years from 1980 through 2013. The data in the bar graph can be modeled by f(x)
x
and , in which f(x) and g(x) represent the percentage of high school seniors who applied to more than three colleges x years after 1980. Use these functions to complete parts (a) through (c) below.
=
+ 24
g(x) = 30.8
0.0216x
Percentage of country A High School Seniors Applying to More Than Three Colleges
1980 19901995 200020052010 2013
0
20
40
60
80
Percentage of high school seniors
30
40
44
48
55
63
69
Year
a.
According to the linear model, what percentage of high school seniors applied to more than three colleges in ?
2005
%
49
b.
According to the exponential model, what percentage of high school seniors applied to more than three colleges in ?
2005
% (Round to the nearest percent as needed.)
53
c.
Which function is a better model for the data shown by the bar graph in ?
2005
A.
Exponential model
B.
Linear model
YOU ANSWERED:
50
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11.
12.
The function describes the percentage of information, f(x), that a particular person remembers x weeks after learning the information.
f(x) = 70
+ 30
− 0.5x
a.
Substitute 0 for x and, without using a calculator, find the percentage of information remembered at the moment it is first learned.
b.
Substitute 1 for x and find the percentage of information that is remembered after 1 week.
c. Find the percentage of information that is remembered after weeks.
8
d.
Find the percentage of information that is remembered after one year (52 weeks).
a. At the moment it is first learned, % of the information is remembered.
100.0
(Round to one decimal place as needed.)
b. After one week, % of the information is remembered.
72.5
(Round to one decimal place as needed.)
c. After weeks, % of the information is remembered.
eight
31.3
(Round to one decimal place as needed.)
d. After one year, % of the information is remembered.
30
(Round to one decimal place as needed.)
YOU ANSWERED:
31.2
You have $
to invest. One bank pays % interest compounded and a second bank pays % interest compounded monthly. Complete parts a and b.
12,000
0.4
quarterly
0.39
a.
Use the formula for compound interest to write a function for the balance in each bank at any time t.
Write a function for the balance in the first bank with interest compounded at any time t.
quarterly
A =
12,000(1.001)
4t
(Simplify your answer. Use integers or decimals for any numbers in the expression. Do not include the $ symbol in your answer.)
Write a function for the balance in the second bank with interest compounded monthly at any time t.
A =
12,000(1.000325)
12t
(Simplify your answer. Use integers or decimals for any numbers in the expression. Do not include the $ symbol in your answer.)
b.
Use a graphing utility to graph both functions in an appropriate viewing rectangle. Based on the graphs, which bank offers the better return on your money?
Graph both functions. Choose the correct graph below. All graphs use a viewing rectangle of [0, 50, 5] by [
, , 500].
12000 17000
A.
B.
C.
D.
Which bank offers the better return on your money?
A.
The bank offers the better return.
second
B.
The bank offers the better return.
first
C.
There is no difference between the two banks.