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Math Problems
Algebra 1
Exponential growth and decay: word problems
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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A savings account earns an interest rate of
2.75
%
2.75 \%
2.75%
compounded monthly for an account with an initial deposit of
$
5
,
000
\$ 5,000
$5
,
000
. How much money will be in the account after
8
8
8
years? Round your answer to the nearest hundredth.
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ctice Quiz Final [CA]
\newline
possible
\newline
A waitress sold
10
10
10
ribeye steak dinners and
26
26
26
grilled salmon dinners, totaling
$
585.15
\$ 585.15
$585.15
on a particular day. Another day she sold
25
25
25
ribeye steak dinners and
13
13
13
grilled salmon dinners, totaling
$
580.82
\$ 580.82
$580.82
. How much did each type of dinner cost?
\newline
□
\square
□
and the cost of salmon dinners is
$
\$
$
□
\square
□
.
\newline
The cost of ribeye steak dinners is
$
\$
$
□
\square
□
(Simplify your answer. Round to the nearest hundredth as needed.)
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a book sold
41
,
100
41,100
41
,
100
copies in its first month of release. suppose this represents
6.8
%
6.8\%
6.8%
of the number of copies sold to date. how many copies have been sold to date? round your answer to the nearest whole number
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1
1
1
point
\newline
A philanthropist pledges to donate
11
%
11 \%
11%
of a fund each year. If the fund initially has
$
790000.00
\$ 790000.00
$790000.00
, how much will the fund have after
10
10
10
years?
\newline
\$ type your añswer...
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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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Question
6
6
6
: A local university has a current enrollment of
10
10
10
,
000
000
000
students. The enrollment is increasing at a rate of
1.5
%
1.5 \%
1.5%
each year. Find the number of years it will take for the population to increase to
12
12
12
,
000
000
000
students?
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Determine the present value of an age-
\newline
90
90
90
lifetime annuity with payments of
80
a
t
t
h
e
e
n
d
o
f
e
a
c
h
y
e
a
r
w
i
t
h
a
n
i
n
t
e
r
e
s
t
r
a
t
e
o
f
80 at the end of each year with an interest rate of
80
a
tt
h
ee
n
d
o
f
e
a
c
h
ye
a
r
w
i
t
hanin
t
eres
t
r
a
t
eo
f
8
8
8
\%
p
e
r
y
e
a
r
i
f
k
n
o
w
n
per year if known
p
erye
a
r
i
f
kn
o
w
n
\ell_{
90
90
90
} =
1000
1000
1000
;
;
;
\ell_{
91
91
91
} =
850
850
850
;
;
;
\ell_{
92
92
92
} =
520
520
520
;
;
;
\ell_{
93
93
93
} =
300
300
300
;
;
;
\ell_{
94
94
94
} =
0
0
0
$.
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The accumulated value of deposits
$
1140
\$1140
$1140
at the end of every
6
6
6
months for four and one-half years when interest is
12
%
12\%
12%
compounded annually
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Rapunzel opens a savings account with
$
900
\$ 900
$900
that earns
9.2
%
9.2 \%
9.2%
interest per year, not compounded.
\newline
How much interest, to the nearest penny, will Rapunzel earn in
9
9
9
years?
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1
1
1
. Anita deposited
$
1100
\$ 1100
$1100
into an account paying
5.1
%
5.1 \%
5.1%
per annum, compounded monthly.
\newline
a. How long will it take for the money to grow to
$
1700
\$ 1700
$1700
? Write your answer as combination of years and months, rounded to the nearest month. (
1
1
1
mark)
\newline
b. b. If the interest was compounded quarterly would it take longer or shorter? Explain. (
2
2
2
marks)
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What amount of money must you invest at
6.8
%
6.8\%
6.8%
compounded monthly, in order to have
$
10
,
000
\$10,000
$10
,
000
after
10
10
10
years? Round your answer to the nearest dollar.
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6
6
6
. Elaine invests
$
3000
\$ 3000
$3000
in an account that pays interest at
2.8
%
2.8 \%
2.8%
per annum, compounding monthly. She makes an additional payment of
$
200
\$ 200
$200
each month. What is the value of the investment after
6
6
6
years? Round your answer to the nearest cent.
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Find the value.
$
3933
\$3933
$3933
invested for
4
4
4
years at
5
%
5\%
5%
compounded quarterly
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Katie won a lottery. She will have a choice of receiving
$
25
,
000
\$25,000
$25
,
000
at the end of each year for the next
30
30
30
years, or a lump sum today. If she can earn a return of
10
10
10
per cent on any investment she makes, what is the minimum amount she should be willing to accept today as a lump-sum payment? (Round to the nearest dollars.)
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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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5
5
5
. Determine the compound interest earned on each investmen
\newline
a)
$
920
\$ 920
$920
compounded weekly at
10.4
%
10.4 \%
10.4%
per annum for
4
4
4
years
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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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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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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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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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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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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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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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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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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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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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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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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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