Resources

Resources

Exponential growth and decay: word problems

150

bacteria doubles in size every

48

hours. What will the population be

144

hours from now?

If a town with a population of \(500\) doubles in size every \(9\) years, what will the population be \(36\) years from now?

If a town with a population of

10,000

doubles in size every

17

years, what will the population be

68

?

The value of a machine was reduced by

36\%

2

years. What is the rate of depreciation per year?

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6\%

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18\%

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20\%

\newline

36\%

A candle is made of

17

ounces of wax. When the candle is burning, the amount of wax in the candle decreases by

1

4

6

ounces of wax remain in this candle, for many hours has it been burning?

Nana is shrinking! Her height decreases by

25 \mathrm{~mm}

\newline

What is her total change in height over

3

\newline

\mathrm{mm}

80

grams of a radioactive kind of tellurium. How much will be left after

8

months if its half-life is

2

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The half-life of a radioactive kind of praseodymium is

17

minutes. If you start with

56

grams of it, how much will be left after

34

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An empty pool has the capacity to hold

2700 \text{ cubic feet } (\text{ft}^3)

of water. A particular hose fills this pool with water at a rate of

25\text{ft}^3

per minute. If the hose is placed into the empty pool and turned on, approximately what percent of the pool will be filled with water after

1

To find the population of a city next year, we multiply its current population by

0

96

. By what percent does the population decrease per year?

\newline

\%

The population of a city increases by

1 \%

per year. What should we multiply the current population by to find the next year's population in one step?

\newline

The population of a city increases by

1 \%

per year. If this year's population is

p

, which expression represents next year's population?

\newline

0.01 p

\newline

1 p

\newline

1.01 p

\newline

1.001 p

The population of a city decreases by

3 \%

per year. If this year's population is

p

, which expression represents next year's population?

\newline

0.97 p

\newline

3 p

\newline

0.997 p

\newline

0.03 p

The population of a city increases by

3 \%

per year. If this year's population is

p

, which expression represents next year's population?

\newline

0.03 p

\newline

3 p

\newline

1.003 p

\newline

1.03 p

Anthony invests money in an account paying a simple interest of

1 \%

m

represents the amount of money he invests, which expression represents his balance after a year, assuming he makes no additional withdrawals or deposits?

\newline

1 m

\newline

1.01 \mathrm{~m}

\newline

1.001 \mathrm{~m}

\newline

0.01 \mathrm{~m}

The population of a city decreases by

5 \%

per year. If this year's population is

p

, which expression represents next year's population?

\newline

0.995 p

\newline

0.95 p

\newline

5 p

\newline

0.05 p

The population of a city increases by

4 \%

per year. If this year's population is

p

, which expression represents next year's population?

\newline

1+0.04

\newline

4 p

\newline

1+0.04 p

\newline

1.04 p

Now the time is

4:45

pm will it be after

2

25

A cell doubles every hour. If there are

2

cells initially, how many cells will there be after

3

An element with mass

780

grams decays by

16.3 \%

per minute. How much of the element is remaining after

16

minutes, to the nearest

10

An element with a mass of

910

grams decays by

27.4 \%

per minute. To the nearest minute, how long will it be until there are

10

grams of the element remaining?

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A radioactive compound with mass

180

grams decays at a rate of

4 \%

per hour. Which equation represents how many grams of the compound will remain after

8

\newline

C=180(0.96)^{8}

\newline

C=180(1-0.04)(1-0.04)(1-0.04)

\newline

C=180(1+0.04)^{8}

\newline

C=180(1-0.4)^{8}

An element with mass

650

grams decays by

29.5 \%

per minute. How much of the element is remaining after

20

minutes, to the nearest

10

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A town has a population of

120

900

and shrinks at a rate of

4.7 \%

every year. Which equation represents the town's population after

8

\newline

P=120,900(1-0.047)

\newline

P=120,900(1+0.047)^{8}

\newline

P=120,900(1-0.47)^{8}

\newline

P=120,900(0.953)^{8}

Isaiah has a collection of vintage action figures that is worth

\$ 210

. If the collection appreciates at a rate of

12.1 \%

per year, which equation represents the value of the collection after

3

\newline

V=210(1-0.121)^{3}

\newline

V=210(1+0.121)

\newline

V=210(0.121)^{3}

\newline

V=210(1+0.121)(1+0.121)(1+0.121)

A new car is purchased for

20

000

dollars. The value of the car depreciates at a rate of

3.7 \%

per year. Which equation represents the value of the car after

3

\newline

V=20,000(1-0.037)

\newline

V=20,000(0.63)^{3}

\newline

V=20,000(0.963)(0.963)(0.963)

\newline

V=20,000(1.037)^{3}

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. Khalil's account has gone into overdraft. His balance is

\$-40.59

. To get back to a positive balance, he plans to deposit money at a steady rate of

\$ 31.02

per week. How much will be in his account after

5

\newline

\$

Tritium, a radioactive isotope of hydrogen, is often used in emergency EXIT signs. Because of the radioactive substance present in these signs, proper disposal is a matter of concern to the Environmental Protection Agency. The half-life of tritium is approximately

12

years. That is, every

12

years, the amount of tritium decreases by

50\%

. If a new tritium EXIT sign contains

25

curies of tritium, approximately how many curies of tritium will remain after

24

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1

\newline

6.25

\newline

12.5

\newline

25

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30

The mass of an isotope decreases at a rate that is proportional to the mass at that time.

\newline

The mass of the isotope was

40

grams initially, and it was

10

16

\newline

What was the mass of the isotope after

20

\newline

Round to the nearest gram.

\newline

\square

Tommy can exchange

8

11

\newline

At this rate, how many dollars can Tommy get with

12

\newline

13 \mathrm{~km}

stretch of road needs repairs. Workers can repair

3 \frac{1}{2} \mathrm{~km}

of road per week.

\newline

How many weeks will it take to repair this stretch of road?

\newline

The double number lines show the ratio of feet to miles.

\newline

How many feet are in

3

\newline

Agent Hunt is transferring classified files from the CIA mainframe into his flash drive.

\newline

S

represents the size of the files on the drive (in megabytes) after

t

\newline

S=5 t+45

\newline

How many megabytes are transferred every

10

\newline

How much of a radioactive kind of chromium will be left after

3

months if you start with

64

grams and the half-life is

1

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