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Math Problems
Algebra 1
Exponential growth and decay: word problems
A new car is purchased for
22300
22300
22300
dollars. The value of the car depreciates at
7
%
7 \%
7%
per year. To the nearest tenth of a year, how long will it be until the value of the car is
8200
8200
8200
dollars?
\newline
Answer:
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4100
4100
4100
dollars is placed in an account with an annual interest rate of
6.5
%
6.5 \%
6.5%
. To the nearest tenth of a year, how long will it take for the account value to reach
18400
18400
18400
dollars?
\newline
Answer:
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A new car is purchased for
17600
17600
17600
dollars. The value of the car depreciates at
7.75
%
7.75 \%
7.75%
per year. To the nearest tenth of a year, how long will it be until the value of the car is
6
6
6
ooo dollars?
\newline
Answer:
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A new car is purchased for
17300
17300
17300
dollars. The value of the car depreciates at
6.5
%
6.5 \%
6.5%
per year. To the nearest year, how long will it be until the value of the car is
10600
10600
10600
dollars?
\newline
Answer:
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An element with a mass of
870
870
870
grams decays by
18.3
%
18.3 \%
18.3%
per minute. To the nearest minute, how long will it be until there are
60
60
60
grams of the element remaining?
\newline
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4500
4500
4500
dollars is placed in an account with an annual interest rate of
7
%
7 \%
7%
. To the nearest tenth of a year, how long will it take for the account value to reach
12800
12800
12800
dollars?
\newline
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4400
4400
4400
dollars is placed in an account with an annual interest rate of
5
%
5 \%
5%
. To the nearest year, how long will it take for the account value to reach
8600
8600
8600
dollars?
\newline
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A new car is purchased for
24300
24300
24300
dollars. The value of the car depreciates at
5.25
%
5.25 \%
5.25%
per year. To the nearest tenth of a year, how long will it be until the value of the car is
13000
13000
13000
dollars?
\newline
Answer:
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A new car is purchased for
$
50
,
000
\$ 50,000
$50
,
000
and over time its value depreciates by one half every
3
3
3
.
5
5
5
years. What is the value of the car
22
22
22
years after it was purchased, to the nearest hundred dollars?
\newline
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A new car is purchased for
$
44
,
000
\$ 44,000
$44
,
000
and over time its value depreciates by one half every
5
5
5
years. What is the value of the car
24
24
24
years after it was purchased, to the nearest hundred dollars?
\newline
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You want to purchase a new car in
6
6
6
years and expect the car to cost
$
10
,
000
\$ 10,000
$10
,
000
. Your bank offers a plan with a guaranteed APR of
6.5
%
6.5 \%
6.5%
if you make regular monthly deposits. How much should you deposit each month to end up with
$
10
,
000
\$ 10,000
$10
,
000
in
6
6
6
years?
\newline
You should invest
$
□
\$ \square
$
□
each month.
\newline
(Round the final answer to the nearest cent as needed. Round all intermediate values to seven decimal places as needed.)
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Calculate the current yield on the described bond.
\newline
A
$
500
\$ 500
$500
Treasury bond with a coupon rate of
4.9
%
4.9 \%
4.9%
that has a market value of
$
425
\$ 425
$425
\newline
The current yield is
□
%
\square \%
□
%
. (Round to two decimal places as needed.)
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Calculate the current yield on the described bond.
\newline
A
$
1000
\$ 1000
$1000
Treasury bond with a coupon rate of
2.4
%
2.4 \%
2.4%
that has a market value of
$
900
\$ 900
$900
\newline
The current yield is
□
%
\square \%
□
%
. (Round to two decimal places as needed.)
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If you bought a stock last year for a price of
$
141
\$ 141
$141
, and it has risen
13
%
13 \%
13%
since then, how much is the stock worth now, to the nearest cent?
\newline
Answer:
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If you bought a stock last year for a price of
$
119
\$ 119
$119
, and it has gone down
3.2
%
3.2 \%
3.2%
since then, how much is the stock worth now, to the nearest cent?
\newline
Answer:
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If you bought a stock last year for a price of
$
96
\$ 96
$96
, and it has risen
16.6
%
16.6 \%
16.6%
since then, how much is the stock worth now, to the nearest cent?
\newline
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You are at a restaurant and the check comes to a total of
$
17
\$ 17
$17
. If you want to leave a
16
%
16 \%
16%
tip, how much total money should you pay, to the nearest cent?
\newline
Answer:
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If you bought a stock last year for a price of
$
53
\$ 53
$53
, and it has gone down
19
%
19 \%
19%
since then, how much is the stock worth now, to the nearest cent?
\newline
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You are at a restaurant and the check comes to a total of
$
35
\$ 35
$35
. If you want to leave a
20
%
20 \%
20%
tip, how much total money should you pay, to the nearest cent?
\newline
Answer:
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If you bought a stock last year for a price of
$
82
\$ 82
$82
, and it has gone down
18
%
18 \%
18%
since then, how much is the stock worth now, to the nearest cent?
\newline
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If you bought a stock last year for a price of
$
108
\$ 108
$108
, and it has risen
9
%
9 \%
9%
since then, how much is the stock worth now, to the nearest cent?
\newline
Answer:
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If you bought a stock last year for a price of
$
134
\$ 134
$134
, and it has gone down
17.5
%
17.5 \%
17.5%
since then, how much is the stock worth now, to the nearest cent?
\newline
Answer:
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If you bought a stock last year for a price of
$
71
\$ 71
$71
, and it has risen
9.6
%
9.6 \%
9.6%
since then, how much is the stock worth now, to the nearest cent?
\newline
Answer:
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If you bought a stock last year for a price of
$
114
\$ 114
$114
, and it has risen
14
%
14 \%
14%
since then, how much is the stock worth now, to the nearest cent?
\newline
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If you bought a stock last year for a price of
$
47
\$ 47
$47
, and it has risen
18.7
%
18.7 \%
18.7%
since then, how much is the stock worth now, to the nearest cent?
\newline
Answer:
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If you bought a stock last year for a price of
$
117
\$ 117
$117
, and it has risen
5
%
5 \%
5%
since then, how much is the stock worth now, to the nearest cent?
\newline
Answer:
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If you bought a stock last year for a price of
$
24
\$ 24
$24
, and it has gone down
7.8
%
7.8 \%
7.8%
since then, how much is the stock worth now, to the nearest cent?
\newline
Answer:
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If you bought a stock last year for a price of
$
54
\$ 54
$54
, and it has risen
1.9
%
1.9 \%
1.9%
since then, how much is the stock worth now, to the nearest cent?
\newline
Answer:
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If you bought a stock last year for a price of
$
80
\$ 80
$80
, and it has risen
2.9
%
2.9 \%
2.9%
since then, how much is the stock worth now, to the nearest cent?
\newline
Answer:
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You are at a restaurant and the check comes to a total of
$
67
\$ 67
$67
. If you want to leave a
19
%
19 \%
19%
tip, how much total money should you pay, to the nearest cent?
\newline
Answer:
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If you are buying at item at a store for a price of
$
25
\$ 25
$25
, and there is a
6.9
%
6.9 \%
6.9%
tax added on top, what would be the total amount due at the register, to the nearest cent?
\newline
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You are at a restaurant and the check comes to a total of
$
18
\$ 18
$18
. If you want to leave a
19
%
19 \%
19%
tip, how much total money should you pay, to the nearest cent?
\newline
Answer:
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If you bought a stock last year for a price of
$
125
\$ 125
$125
, and it has gone down
14
%
14 \%
14%
since then, how much is the stock worth now, to the nearest cent?
\newline
Answer:
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When a number is decreased by
5
%
5 \%
5%
, the result is
50
50
50
. What is the original number to the nearest tenth?
\newline
Answer:
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In the year
2000
2000
2000
, a person bought a new car for
$
16500
\$ 16500
$16500
. For each consecutive year after that, the value of the car depreciated by
6
%
6 \%
6%
. How much would the car be worth in the year
2003
2003
2003
, to the nearest hundred dollars?
\newline
Answer:
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In the year
2001
2001
2001
, a person bought a new car for
$
17000
\$ 17000
$17000
. For each consecutive year after that, the value of the car depreciated by
10
%
10 \%
10%
. How much would the car be worth in the year
2003
2003
2003
, to the nearest hundred dollars?
\newline
Answer:
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In the year
2004
2004
2004
, a person bought a new car for
$
15500
\$ 15500
$15500
. For each consecutive year after that, the value of the car depreciated by
10
%
10 \%
10%
. How much would the car be worth in the year
2006
2006
2006
, to the nearest hundred dollars?
\newline
Answer:
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In the year
2009
2009
2009
, a person bought a new car for
$
17000
\$ 17000
$17000
. For each consecutive year after that, the value of the car depreciated by
8
%
8 \%
8%
. How much would the car be worth in the year
2011
2011
2011
, to the nearest hundred dollars?
\newline
Answer:
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In the year
2008
2008
2008
, a person bought a new car for
$
24500
\$ 24500
$24500
. For each consecutive year after that, the value of the car depreciated by
11
%
11 \%
11%
. How much would the car be worth in the year
2012
2012
2012
, to the nearest hundred dollars?
\newline
Answer:
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In the year
2006
2006
2006
, a person bought a new car for
$
30000
\$ 30000
$30000
. For each consecutive year after that, the value of the car depreciated by
8
%
8 \%
8%
. How much would the car be worth in the year
2010
2010
2010
, to the nearest hundred dollars?
\newline
Answer:
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In the year
2004
2004
2004
, a person bought a new car for
$
28000
\$ 28000
$28000
. For each consecutive year after that, the value of the car depreciated by
13
%
13 \%
13%
. How much would the car be worth in the year
2007
2007
2007
, to the nearest hundred dollars?
\newline
Answer:
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In the year
2004
2004
2004
, a person bought a new car for
$
16000
\$ 16000
$16000
. For each consecutive year after that, the value of the car depreciated by
13
%
13 \%
13%
. How much would the car be worth in the year
2006
2006
2006
, to the nearest hundred dollars?
\newline
Answer:
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In the year
2006
2006
2006
, a person bought a new car for
$
24000
\$ 24000
$24000
. For each consecutive year after that, the value of the car depreciated by
9
%
9 \%
9%
. How much would the car be worth in the year
2008
2008
2008
, to the nearest hundred dollars?
\newline
Answer:
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In the year
2002
2002
2002
, a person bought a new car for
$
18500
\$ 18500
$18500
. For each consecutive year after that, the value of the car depreciated by
7
%
7 \%
7%
. How much would the car be worth in the year
2004
2004
2004
, to the nearest hundred dollars?
\newline
Answer:
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A town has a population of
14000
14000
14000
and grows at
3
%
3 \%
3%
every year. What will be the population after
14
14
14
years, to the nearest whole number?
\newline
Answer:
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A new car is purchased for
24900
24900
24900
dollars. The value of the car depreciates at
13.75
%
13.75 \%
13.75%
per year. What will the value of the car be, to the nearest cent, after
14
14
14
years?
\newline
Answer:
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A new car is purchased for
19400
19400
19400
dollars. The value of the car depreciates at
13.5
%
13.5 \%
13.5%
per year. What will the value of the car be, to the nearest cent, after
12
12
12
years?
\newline
Answer:
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A new car is purchased for
24600
24600
24600
dollars. The value of the car depreciates at
13.75
%
13.75 \%
13.75%
per year. What will the value of the car be, to the nearest cent, after
15
15
15
years?
\newline
Answer:
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A new car is purchased for
19600
19600
19600
dollars. The value of the car depreciates at
11.75
%
11.75 \%
11.75%
per year. What will the value of the car be, to the nearest cent, after
14
14
14
years?
\newline
Answer:
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6400
6400
6400
dollars is placed in an account with an annual interest rate of
6.25
%
6.25 \%
6.25%
. How much will be in the account after
20
20
20
years, to the nearest cent?
\newline
Answer:
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