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Math Problems
Algebra 1
Exponential growth and decay: word problems
Jacob invests
$
1049
\$1049
$1049
in a savings account with a fixed annual interest rate of
7
%
7\%
7%
compunded
3
3
3
times per year. What will the account balance be after
10
10
10
years?
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You ask your friend to lend you
$
200
\$200
$200
to buy your favorite toy. She says she can lend you the money only if you give her an extra
$
2
\$2
$2
every month that passes before you return it. What is the total amount you must pay her if you return it after
2
2
2
years? Also, what is the annual rate of interest she is charging you?
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There is a population of
30
30
30
bacteria in a colony. If the number of bacteria doubles every
500
500
500
hours, what will the population be
1
,
000
1,000
1
,
000
hours from now?
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A father is
30
30
30
years older than his son. After
12
12
12
years, the man will be as old as his son. find thir present age.
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A father is
30
30
30
years older than his son. After
12
12
12
years. the man will. be as old as his son. find thir present age.
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Mr. and Mrs. Williams hope to send their daughter to college in thirteen years. How much money should they invest now at an interest rate of
9
%
9 \%
9%
per year, compounded continuously, in order to be able to contribute
$
9500
\$ 9500
$9500
to her education?
\newline
Do not round any intermediate computations, and round your answer to the nearest cent.
\newline
\($\) _____
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A company has the goal of doubling their revenue from
32
32
32
million dollars to
64
64
64
million dollars over the next
2
2
2
years. If the company increases its revenue by
50
%
50\%
50%
in the first year, by approximately what percentage must the company increase their revenue in the second year in order to reach their goal?
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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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Suppose you invest
$
10000
\$ 10000
$10000
at
5.1
%
5.1 \%
5.1%
annual interest, compounded weekly. How long will it take to double your money? Round to the nearest year. (Hint this will be a whole number)
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Becky is
21
21
21
years old and spends
$
175
\$ 175
$175
on cigarettes per month. If she decides to stop smoking, and instead invests this money at the end of every
3
3
3
months into an investment paying
4.25
%
4.25 \%
4.25%
compounded quarterly, how much will she have when she turns
61
61
61
? For full marks your answer(s) should be rounded to the nearest cent.
\newline
Future value
=
$
□
= \$ \square
=
$
□
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A new car is purchased for
20000
20000
20000
dollars. The value of the car depreciates at
12.5
%
12.5\%
12.5%
per year. What will the value of the car be, to the nearest cent, after
11
11
11
years?
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A certain forest covers an area of
4400
km
2
4400\,\text{km}^2
4400
km
2
. Suppose that each year this area decreases by
4.75
%
4.75\%
4.75%
. What will the area be after
10
10
10
years? Use the calculator provided and round your answer to the nearest square kilometer.
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Determine the compound interest earned on each investment
\newline
$
920
\$ 920
$920
compounded weekly at
10.4
%
10.4 \%
10.4%
per annum for
4
4
4
years
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As a result of inflation, the purchasing power of a fixed quantity of money decreases by
5
%
5\%
5%
every year. If a certain quantity of money can buy
940
940
940
frozen dinners this year, how many frozen dinners can it buy in
16
16
16
years?
\newline
If necessary, round your answer to the nearest whole number.
\newline
____ frozen dinners
\newline
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A little-known species of insect is approaching extinction, with a population that falls by
10
%
10\%
10%
every year. There are currently
2
,
400
2,400
2
,
400
insects remaining. How many will there be in
4
4
4
years? If necessary, round your answer to the nearest whole number.
\newline
\newline
_
_
_
_
\_\_\_\_
____
insects
\newline
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Emma pays
$
2
,
600
\$2,600
$2
,
600
for a washer/dryer combo. Each year, the appliance loses
15
%
15\%
15%
of its resale value. How much will it be worth in
4
4
4
years? If necessary, round your answer to the nearest cent.
\newline
$
\$
$
____
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Barry just read that his computer, which costs
$
1
,
300
\$1,300
$1
,
300
new, loses
25
%
25\%
25%
of its value every year. If this estimate is accurate, how much will the computer be worth in
15
15
15
years? If necessary, round your answer to the nearest cent.
\newline
$
\$
$
____
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A nautilus shell is made up of many chambers, each chamber roughly
5
%
5\%
5%
larger than the previous one. Assuming a nautilus creates a new chamber every year, and this year's chamber has a volume of
880
880
880
microliters, how large will the chamber created in
8
8
8
years be? If necessary, round your answer to the nearest tenth.
\newline
\newline
____ microliters
\newline
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A growing farming conglomerate increases its water usage at a rate of
10
%
10\%
10%
every year. If it used
13
,
000
13,000
13
,
000
megaliters of water this year, then how much water will it use
17
17
17
years from now? If necessary, round your answer to the nearest hundredth.
\newline
_
_
_
_
\_\_\_\_
____
megaliters
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Richmond County has a population of
850
,
000
850,000
850
,
000
people, which increases by
10
%
10\%
10%
every year due to a growing tech industry. What will the population be in
2
2
2
years? If necessary, round your answer to the nearest whole number.
\newline
____ people
\newline
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Colleen has put
$
26
,
000
\$26,000
$26
,
000
into a retirement fund. The fund has an estimated annual return of
10
%
10\%
10%
. If Colleen doesn't add any more money, how much can she expect to have in the fund in
7
7
7
years? If necessary, round your answer to the nearest cent.
\newline
$
\$
$
____
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Joel has a vintage comic book worth
$
360
\$360
$360
. According to a dealer, the value of this particular comic book will increase by
5
%
5\%
5%
each year. How much will the comic book be worth in
15
15
15
years?
\newline
If necessary, round your answer to the nearest cent.
\newline
$
\$
$
____
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Belmont is a growing industrial town. Every year, the level of
CO
2
\text{CO}_2
CO
2
emissions from the town increases by
10
%
10\%
10%
. If the town produced
330
,
000
330,000
330
,
000
metric tons of
CO
2
\text{CO}_2
CO
2
this year, how much will be produced
6
6
6
years in the future?
\newline
If necessary, round your answer to the nearest whole number.
\newline
____ metric tons
\newline
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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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Rachel deposited
10
10
10
$
\$
$
in an account earning
5
%
5\%
5%
interest compounded annually. To the nearest cent, how much interest will she earn in
3
3
3
years?
$
\$
$
____
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Rats have recently become a nuisance in Norwood. Efforts to control the rat problem have led to the rat population declining by
15
%
15\%
15%
every year. If the town currently has
13
,
000
13,000
13
,
000
rats, how many rats will there be in
3
3
3
years?
\newline
If necessary, round your answer to the nearest whole number.
\newline
____ rats
\newline
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Eva deposited
50
50
50
$
\$
$
in an account earning
10
%
10\%
10%
interest compounded annually. To the nearest cent, how much interest will she earn in
2
2
2
years?
$
\$
$
____
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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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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 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 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 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 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 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 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
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
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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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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