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Math Problems
Algebra 1
Exponential growth and decay: word problems
Edgar has
30
30
30
$
\$
$
in an account that earns
5
%
5\%
5%
interest compounded annually. To the nearest cent, how much interest will he earn in
2
2
2
years?
$
\$
$
____
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Tritium is a radioactive isotope of hydrogen that decays by about
5
%
5\%
5%
per year. A large bottle of water that contained
450
,
000
450,000
450
,
000
tritium atoms remained undisturbed for
11
11
11
years. How much tritium does the bottle contain now? If necessary, round your answer to the nearest whole number.
\newline
____ tritium atoms
\newline
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Liam can type faster than any of his classmates. He took a test that showed he can type
700
700
700
words in
5
5
5
minutes. At this rate, how long does Liam need to type a
20
20
20
-page paper with
250
250
250
words on each page? Round your answer to the nearest whole minute.
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The population of a town is
500
,
000
500,000
500
,
000
. If the population growth rate is
\newline
6
%
6\%
6%
yearly, when will the population exceed
600
,
000
600,000
600
,
000
? (Express the answer correct to the nearest integer.)
\newline
A.
2
2
2
\newline
B.
3
3
3
\newline
C.
4
4
4
\newline
D.
5
5
5
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Last year at a certain high school, there were
150
150
150
ninth graders on the honor roll and
100
100
100
tenth graders on the honor roll. This year, the number of ninth graders on the honor roll increased by
20
%
20\%
20%
and the number of tenth graders on the honor roll increased by
3
%
3\%
3%
. By what percentage did the total number of students on the honor roll increase? Round your answer to the nearest tenth (if necessary).
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Emma earns a
$
39
,
000
\$ 39,000
$39
,
000
salary in the first year of her career. Each year, she gets a
5
%
5 \%
5%
raise.
\newline
How much does Emma earn in total in the first
11
11
11
years of her career? Round your final answer to the nearest thousand.
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The sales tax in your city is
4.4
%
4.4\%
4.4%
, and an item costs
3
3
3
before tax. How much tax would you pay on that item? Round to the nearest hundredth or cent.
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The population of a city increases by
1.7
%
1.7 \%
1.7%
per year. What should we multiply the current population by to find the next year's population in one step?
\newline
Answer:
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The population of a city decreases by
2
%
2 \%
2%
per year. What should we multiply the current population by to find next year's population in one step?
\newline
Answer:
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The population of a city increases by
5
%
5 \%
5%
per year. What should we multiply the current population by to find the next year's population in one step?
\newline
Answer:
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The population of a city increases by
1.2
%
1.2 \%
1.2%
per year. If this year's population is
98
98
98
,
000
000
000
, what will next year's population be, to the nearest individual?
\newline
Answer:
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The population of a city decreases by
4.1
%
4.1 \%
4.1%
per year. If this year's population is
314
314
314
,
000
000
000
, what will next year's population be, to the nearest individual?
\newline
Answer:
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The population of a city decreases by
2.3
%
2.3 \%
2.3%
per year. If this year's population is
363
363
363
,
000
000
000
, what will next year's population be, to the nearest individual?
\newline
Answer:
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The population of a city increases by
3.3
%
3.3 \%
3.3%
per year. If this year's population is
127
127
127
,
000
000
000
, what will next year's population be, to the nearest individual?
\newline
Answer:
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The population of a city increases by
1.5
%
1.5 \%
1.5%
per year. If this year's population is
268
268
268
,
000
000
000
, what will next year's population be, to the nearest individual?
\newline
Answer:
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The population of a city decreases by
0.9
%
0.9 \%
0.9%
per year. If this year's population is
160
160
160
,
000
000
000
, what will next year's population be, to the nearest individual?
\newline
Answer:
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The population of a city decreases by
2.2
%
2.2 \%
2.2%
per year. If this year's population is
305
305
305
,
000
000
000
, what will next year's population be, to the nearest individual?
\newline
Answer:
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The population of a city decreases by
3
%
3 \%
3%
per year. If this year's population is
p
p
p
, which expression represents next year's population?
\newline
p
−
0.03
p-0.03
p
−
0.03
\newline
1
p
−
0.03
p
1 p-0.03 p
1
p
−
0.03
p
\newline
3
p
3 p
3
p
\newline
0
0
0
.
97
97
97
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Use the appropriate formula to find the future value (in
$
\$
$
) of
$
700
\$700
$700
deposited at the beginning of every six months, for
17
17
17
years if a bank pays
8
%
8\%
8%
interest, compounded semiannually. (Round your answers to the nearest cent.)
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Bacteria in a culture increase at a rate that is proportional at any time to the number of bacteria at that time. There were
800
800
800
bacteria initially, and they triple every
10
10
10
hours. What is the number of bacteria after
4
4
4
hours? Round to the nearest integer.
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Submit test
\newline
How much must be deposited today into the following account in order to have
$
45
,
000
\$ 45,000
$45
,
000
in
7
7
7
years for a down payment on a house? Assume no additional deposits are made.
\newline
An account with monthly compounding and an APR of
6
%
6 \%
6%
\newline
$
\$
$
should be deposited today.
\newline
(Do not round until the final answer. Then round to the nearest cent as needed.)
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7
7
7
) Amit's bank charges a
$
5.75
\$ 5.75
$5.75
fee every month that his account balance is below a certain amount. Amit writes the equation
(
−
5.75
)
×
7
=
40.25
(-5.75) \times 7=40.25
(
−
5.75
)
×
7
=
40.25
to represent how much his account balance changes after
7
7
7
months of fees.
\newline
Is Amit's reasoning correct? Explain.
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eview Unit
6
6
6
\newline
Score:
2
/
10
2 / 10
2/10
\newline
Penalty:
1
1
1
off
\newline
Question
\newline
Show Examples
\newline
A new car is purchased for
17300
17300
17300
dollars. The value of the car depreciates at
9.25
%
9.25 \%
9.25%
pe year. What will the value of the car be, to the nearest cent, after
15
15
15
years?
\newline
Answer Attempt
1
1
1
out of
2
2
2
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Holtzman Clothiers's stock currently sells for
$
36.00
\$36.00
$36.00
a share. It just paid a dividend of
$
1.00
\$1.00
$1.00
a share (i.e.,
D
0
=
$
1.00
D_0 = \$1.00
D
0
=
$1.00
). The dividend is expected to grow at a constant rate of
9
%
9\%
9%
a year. What stock price is expected
1
1
1
year from now?
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MY NOTES
\newline
ASK YOUR TEACHER
\newline
PRACTICE ANOTHER
\newline
A landscape architect accrued
$
7
,
834.39
\$ 7,834.39
$7
,
834.39
in credit card debt. If the architect makes a monthly payment of
$
400
\$ 400
$400
(and makes no additional charges on the account), how many months will it take to repay the debt if the annual interest rate on the credit card is
18.8
%
18.8 \%
18.8%
? (Round your answer up to the nearest month.)
\newline
months
\newline
Need Help?
\newline
Read It
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Suppose you have
$
9500
\$ 9500
$9500
deposited at
2.75
%
2.75 \%
2.75%
compounded semiannually. About long will it take your balanc to increase to
$
10900
\$ 10900
$10900
?
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You can retry this question below
\newline
Suppose you have
$
9500
\$ 9500
$9500
deposited at
2.75
%
2.75 \%
2.75%
compounded semiannually. About long will it take your balance to increase to
$
10900
\$ 10900
$10900
?
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Many bank accounts never go below zero. But some banks will allow a negative balance, at least for a short time, called an overdraft. It means someone has taken out, or 'drafted', more money than was in the account to begin with. Hunter's account has gone into overdraft. His balance is
−
$
19.87
-\$19.87
−
$19.87
. To get back to a positive balance, he plans to deposit money at a steady rate of
$
23.61
\$23.61
$23.61
per week. How much will be in his account after
5
5
5
weeks?
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Charis invested
$
140
\$ 140
$140
. She earned a simple interest of
3
%
3 \%
3%
per year on the initial investment. If no money was added or removed from the investment, what was the amount of interest Charis received at the end of two years?
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Find the simple interest on a loan of
$
18
,
000
\$ 18,000
$18
,
000
at
9.8
%
9.8 \%
9.8%
interest for
9
9
9
months
\newline
$
\$
$
_____
\newline
Give your answer to the nearest cent
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Find the simple interest on a loan of
$
18
,
000
\$ 18,000
$18
,
000
at
9.8
%
9.8 \%
9.8%
interest for
9
9
9
months
\newline
$ ______
\newline
Give your answer to the nearest cent
\newline
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Find the simple interest on a loan of
$
35
,
000
\$ 35,000
$35
,
000
at
9
%
9 \%
9%
interest for
10
10
10
months
\newline
$
\$
$
___________
\newline
Give your answer to the nearest cent
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A piece of land was purchased for
$
65
,
000
\$ 65,000
$65
,
000
. The value of the land has slowly been decreasing by
1
%
1 \%
1%
annually. How much will the land be worth in
20
20
20
years? Round your answer to the nearest dollar.
\newline
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The sales tax in your city is
4.4
%
4.4 \%
4.4%
, and an item costs
$
3
\$ 3
$3
before tax.
\newline
How much tax would you pay on that item?
\newline
Round to the nearest hundredth or cent.
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Suppose a man is dead at the age
90
90
90
its was the
2009
2009
2009
, and what would be the age when its was
1986
1986
1986
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An investment company pays
6
%
6\%
6%
compounded semiannually. You want to have
$
17
,
000
\$17,000
$17
,
000
in the future.
\newline
(A) How much should you deposit now to have that amount
5
5
5
years from now?
\newline
$
\$
$
□
\square
□
(Round to the nearest cent.)
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Find the amount that results from the investment. Round to the nearest cent.
\newline
$
14
,
000
\$14,000
$14
,
000
invested at
15
%
15\%
15%
compounded semiannually after a period of
8
8
8
years
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Find the effective rate of interest. Round to three decimal places.
\newline
85
%
85\%
85%
compounded daily
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In a recent year,
26.6
%
26.6\%
26.6%
of all registered doctors were female. If there were
58
,
600
58,600
58
,
600
female registered doctors that year, what was the total number of registered doctors?
\newline
Round your answer to the nearest whole number.
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ion list
\newline
How much money should be deposited today in an account that earns
\newline
3
%
3\%
3%
compounded semiannually so that it will accumulate to
\newline
$
12
,
000
\$12,000
$12
,
000
in three years?
\newline
(i) Click the icon to view some finance formulas.
\newline
The amount of money that should be deposited is
\newline
$
\$
$
□
\square
□
.
\newline
(Round up to the nearest cent.)
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Finding the initial amount in a word problem on continuous compound...
\newline
How much should be Invested now at an interest rate of
\newline
6
%
6\%
6%
per year, compounded continuously, to have
\newline
$
2000
\$2000
$2000
in five years?
\newline
Do not round any Intermediate computations, and round your answer to the nearest cent.
\newline
$
∏
\$\prod
$
∏
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On the first day it was posted online, a music video got
1000
1000
1000
views. The number of views that the video got each day increased by
20
%
20 \%
20%
per day. How many total views did the video get over the course of the first
24
24
24
days, to the nearest whole number?
\newline
Answer:
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On the first day it was posted online, a music video got
310
310
310
views. The number of views that the video got each day increased by
20
%
20 \%
20%
per day. How many total views did the video get over the course of the first
6
6
6
days, to the nearest whole number?
\newline
Answer:
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In a company's first year in operation, it made an annual profit of
$
129
,
000
\$ 129,000
$129
,
000
. The profit of the company increased at a constant
25
%
25 \%
25%
per year each year. How much total profit would the company make over the course of its first
8
8
8
years of operation, to the nearest whole number?
\newline
Answer:
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An author published a book which was being sold online. The first month the author sold
28500
28500
28500
books, but the sales were declining steadily at
14
%
14 \%
14%
each month. If this trend continues, how many total books would the author have sold over the first
16
16
16
months, to the nearest whole number?
\newline
Answer:
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An author published a book which was being sold online. The first month the author sold
8000
8000
8000
books, but the sales were declining steadily at
9
%
9 \%
9%
each month. If this trend continues, how many total books would the author have sold over the first
21
21
21
months, to the nearest whole number?
\newline
Answer:
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A small country emits
70
70
70
,
000
000
000
kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by
1.4
%
1.4 \%
1.4%
per year for the next
6
6
6
years. In the first year of the agreement, the country will keep its emissions at
70
70
70
,
000
000
000
kilotons and the emissions will decrease
1.4
%
1.4 \%
1.4%
in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the
6
6
6
year period, to the nearest whole number?
\newline
Answer:
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Nabhitha was offered a job that paid a salary of
$
83
,
000
\$ 83,000
$83
,
000
in its first year. The salary was set to increase by
5
%
5 \%
5%
per year every year. If Nabhitha worked at the job for
26
26
26
years, what was the total amount of money earned over the
26
26
26
years, to the nearest whole number?
\newline
Answer:
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A major fishing company does its fishing in a local lake. The first year of the company's operations it managed to catch
170
170
170
,
000
000
000
fish. Due to population decreases, the number of fish the company was able to catch decreased by
6
%
6 \%
6%
each year. How many total fish did the company catch over the first
11
11
11
years, to the nearest whole number?
\newline
Answer:
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Tyee was offered a job that paid a salary of
$
76
,
000
\$ 76,000
$76
,
000
in its first year. The salary was set to increase by
3
%
3 \%
3%
per year every year. If Tyee worked at the job for
10
10
10
years, what was the total amount of money earned over the
10
10
10
years, to the nearest whole number?
\newline
Answer:
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