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Math Problems
Algebra 1
Exponential growth and decay: word problems
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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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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On the first day it was posted online, a music video got
2000
2000
2000
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
30
30
30
days, 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
70
70
70
,
000
000
000
fish. Due to population decreases, the number of fish the company was able to catch decreased by
3
%
3 \%
3%
each year. How many total fish did the company catch over the first
10
10
10
years, to the nearest whole number?
\newline
Answer:
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Salma just started a running plan where she runs
16
16
16
miles the first week and then increases the number of miles she runs by
5
%
5 \%
5%
each week. If she keeps up this plan for
6
6
6
weeks, how many total miles would Salma have run, 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
$
226
,
000
\$ 226,000
$226
,
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
13
13
13
years of operation, 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
$
391
,
500
\$ 391,500
$391
,
500
. The profit of the company increased at a constant
18
%
18 \%
18%
per year each year. How much total profit would the company make over the course of its first
6
6
6
years of operation, 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
8
%
8 \%
8%
each year. How many total fish did the company catch over the first
16
16
16
years, to the nearest whole number?
\newline
Answer:
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Nachelle just started a running plan where she runs
8
8
8
miles the first week and then increases the number of miles she runs by
5
%
5 \%
5%
each week. If she keeps up this plan for
18
18
18
weeks, how many total miles would Nachelle have run, to the nearest whole number?
\newline
Answer:
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Nakeisha just started a running plan where she runs
7
7
7
miles the first week and then increases the number of miles she runs by
10
%
10 \%
10%
each week. If she keeps up this plan for
25
25
25
weeks, how many total miles would Nakeisha have run, 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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Kehlani was offered a job that paid a salary of
$
44
,
000
\$ 44,000
$44
,
000
in its first year. The salary was set to increase by
5
%
5 \%
5%
per year every year. If Kehlani worked at the job for
11
11
11
years, what was the total amount of money earned over the
11
11
11
years, to the nearest whole number?
\newline
Answer:
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In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment the mass of the substance was
1500
1500
1500
grams and mass was decreasing by
13
%
13 \%
13%
per day. Determine the mass of the radioactive sample at the beginning of the
13
13
13
th day of the experiment. Round to the nearest tenth (if necessary).
\newline
Answer:
□
\square
□
grams
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Savannah invested
$
1500
\$ 1500
$1500
in an account that pays
3
%
3 \%
3%
interest compounded annually. Assuming no deposits or withdrawals are made, find how much money Savannah would have in the account
20
20
20
years after her initial investment. Round your answer to the nearest whole number.
\newline
Answer: $ \(\square\)
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You rent an apartment that costs
$
900
\$ 900
$900
per month during the first year, but the rent is set to go up
12.5
%
12.5 \%
12.5%
per year. What would be the rent of the apartment during the
6
6
6
th year of living in the apartment? Round your answer to the nearest whole number.
\newline
Answer:
$
\$
$
□
\square
□
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You rent an apartment that costs
$
1400
\$ 1400
$1400
per month during the first year, but the rent is set to go up
10
%
10 \%
10%
per year. What would be the rent of the apartment during the
9
9
9
th year of living in the apartment? Round your answer to the nearest whole number.
\newline
Answer:
$
\$
$
□
\square
□
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In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment the mass of the substance was
1000
1000
1000
grams and mass was decreasing by
9
%
9 \%
9%
per day. Determine the mass of the radioactive sample at the beginning of the
12
12
12
th day of the experiment. Round to the nearest tenth (if necessary).
\newline
Answer:
□
\square
□
grams
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In a lab experiment, the decay of a radioactive isotope is being observed. At the beginning of the first day of the experiment the mass of the substance was
1400
1400
1400
grams and mass was decreasing by
12
%
12 \%
12%
per day. Determine the mass of the radioactive sample at the beginning of the
18
18
18
th day of the experiment. Round to the nearest tenth (if necessary).
\newline
Answer:
□
\square
□
grams
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You rent an apartment that costs
$
1700
\$ 1700
$1700
per month during the first year, but the rent is set to go up
10
10
10
\% per year. What would be the rent of the apartment during the
10
10
10
th year of living in the apartment? Round your answer to the nearest whole number.
\newline
Answer:
$
\$
$
□
\square
□
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A new car is purchased for
15300
15300
15300
dollars. The value of the car depreciates at
14.25
%
14.25 \%
14.25%
per year. What will the value of the car be, to the nearest cent, after
6
6
6
years?
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If
$
2
,
000
\$ 2,000
$2
,
000
is invested at
5
%
5 \%
5%
compounded quarterly, what is the amount after
8
8
8
years?
\newline
The amount after
8
8
8
years will be
$
□
\$ \square
$
□
.
\newline
(Round to the nearest cent.)
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The real risk-free rate is
3.0
%
3.0\%
3.0%
and inflation is expected to be
3.25
%
3.25\%
3.25%
for the next
2
2
2
years. A
2
2
2
-year Treasury security yields
6.55
%
6.55\%
6.55%
. What is the maturity risk premium for the
2
2
2
-year security?
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An analyst is evaluating securities in a developing nation where the inflation rate is very high. As a result, the analyst has been warned not to ignore the cross-product between the real rate and inflation. A
6
6
6
-year security with no maturity, default, or liquidity risk has a yield of
16.60
%
16.60\%
16.60%
. If the real risk-free rate is
6
%
6\%
6%
, what average rate of inflation is expected in this country over the next
6
6
6
years?
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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
.
5
5
5
years. What is the value of the car
9
9
9
years after it was purchased, to the nearest hundred dollars?
\newline
Answer:
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A person invested
$
9
,
000
\$ 9,000
$9
,
000
in an account growing at a rate allowing the money to double every
10
10
10
years. How much money would be in the account after
19
19
19
years, to the nearest dollar?
\newline
Answer:
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A person invested
$
1
,
100
\$ 1,100
$1
,
100
in an account growing at a rate allowing the money to double every
15
15
15
years. How much money would be in the account after
6
6
6
years, to the nearest dollar?
\newline
Answer:
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A new car is purchased for
$
42
,
000
\$ 42,000
$42
,
000
and over time its value depreciates by one half every
3
3
3
years. What is the value of the car
10
10
10
years after it was purchased, to the nearest hundred dollars?
\newline
Answer:
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A person invested
$
450
\$ 450
$450
in an account growing at a rate allowing the money to double every
6
6
6
years. How much money would be in the account after
28
28
28
years, to the nearest dollar?
\newline
Answer:
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A new car is purchased for
16400
16400
16400
dollars. The value of the car depreciates at
6.75
%
6.75 \%
6.75%
per year. To the nearest year, how long will it be until the value of the car is
8500
8500
8500
dollars?
\newline
Answer:
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4900
4900
4900
dollars is placed in an account with an annual interest rate of
5.25
%
5.25 \%
5.25%
. To the nearest tenth of a year, how long will it take for the account value to reach
13200
13200
13200
dollars?
\newline
Answer:
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A new car is purchased for
18600
18600
18600
dollars. The value of the car depreciates at
14
%
14 \%
14%
per year. To the nearest tenth of a year, how long will it be until the value of the car is
6800
6800
6800
dollars?
\newline
Answer:
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7600
7600
7600
dollars is placed in an account with an annual interest rate of
6.25
%
6.25 \%
6.25%
. To the nearest year, how long will it take for the account value to reach
16000
16000
16000
dollars?
\newline
Answer:
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A town has a population of
9000
9000
9000
and grows at
5
%
5 \%
5%
every year. To the nearest year, how long will it be until the population will reach
18900
18900
18900
?
\newline
Answer:
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A town has a population of
7000
7000
7000
and grows at
3.5
%
3.5 \%
3.5%
every year. To the nearest tenth of a year, how long will it be until the population will reach
9400
9400
9400
?
\newline
Answer:
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An element with a mass of
350
350
350
grams decays by
6.6
%
6.6 \%
6.6%
per minute. To the nearest minute, how long will it be until there are
230
230
230
grams of the element remaining?
\newline
Answer:
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8700
8700
8700
dollars is placed in an account with an annual interest rate of
8
%
8 \%
8%
. To the nearest year, how long will it take for the account value to reach
20000
20000
20000
dollars?
\newline
Answer:
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A new car is purchased for
22300
22300
22300
dollars. The value of the car depreciates at
12.25
%
12.25 \%
12.25%
per year. To the nearest tenth of a year, how long will it be until the value of the car is
3700
3700
3700
dollars?
\newline
Answer:
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5200
5200
5200
dollars is placed in an account with an annual interest rate of
5.75
%
5.75 \%
5.75%
. To the nearest year, how long will it take for the account value to reach
22500
22500
22500
dollars?
\newline
Answer:
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5800
5800
5800
dollars is placed in an account with an annual interest rate of
6.25
%
6.25 \%
6.25%
. To the nearest year, how long will it take for the account value to reach
27500
27500
27500
dollars?
\newline
Answer:
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A town has a population of
13000
13000
13000
and grows at
2
%
2 \%
2%
every year. To the nearest tenth of a year, how long will it be until the population will reach
21200
21200
21200
?
\newline
Answer:
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3300
3300
3300
dollars is placed in an account with an annual interest rate of
8.25
%
8.25 \%
8.25%
. To the nearest tenth of a year, how long will it take for the account value to reach
7500
7500
7500
dollars?
\newline
Answer:
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7600
7600
7600
dollars is placed in an account with an annual interest rate of
7.5
%
7.5 \%
7.5%
. To the nearest tenth of a year, how long will it take for the account value to reach
34700
34700
34700
dollars?
\newline
Answer:
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A new car is purchased for
22100
22100
22100
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
12600
12600
12600
dollars?
\newline
Answer:
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