Resources

Resources

Exponential growth and decay: word problems

A biologist puts a certain number of DNA strands into a machine, which uses a process called PCR cycling. Each PCR cycle, the machine creates a copy of every DNA strand. All of the DNA strands (the original DNA strands and their coples) remain together in the machine, ready for more PCR cycles. If a biologist puts

1

thousand DNA strands into the machine and runs it for

4

cycles, how many DNA strands will be in the machine at the end of the process, in thousands?

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If the number of bacteria in a colony doubles every

203

minutes and there is currently a population of

40

bacteria, what will the population be

812

minutes from now

?

A city doubles its size every

5

years. If the population is currently

469,900

, what will the population be in

20

?

6

. A zircon crystal is measured for age using uranium

-235

-207

decay (half-life is

704

million years). Assuming that there was no lead

207

initially, and you measure the elemental composition and find

35

000

000

-207

1

100

000

-235

atoms, how old is the zircon crystal?

25

years ago a man was

87

times as old as his son. After

5

years the father will be

3

time as old as his son. Find their present age.

There are two cubes. The first cube has a volume of

1,000

cubic units. The second cube is smaller than the first, with sides only half as long. What is the volume of the second cube?

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The sum of a geometric series whose first three terms are

8000

-12000

18000

57875

. What is the last term of the series?

California is the largest U.S. producer of honey, with an annual yield of

3 \times 10^7

pounds. How many millions of pounds is that?

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Dane is using two differently sized water pumps to clean up flooded water. The larger pump can remove the water alone in

240\,\text{min}

. The smaller pump can remove the water alone in

400\,\text{min}

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How long would it take the pumps to remove the water working together?

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\square\,\text{minutes}

During randomized human trials for the chemical compound G

-23

Paxilon Hydrochlorate,

0.1\%

of trial participants exhibited unpleasant side effects. At this rate, if a population of

5,200,000

is exposed to the compound, how many people would be expected to exhibit similar side effects?

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2

10 \mathrm{~L}

20

seconds. What is the rate of flow in litres per hour?

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0

0001

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30

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1800

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7200

Today, the population of Canyon Falls is

22

500

and the population of Swift Creek is

15

200

. The population of Canyon Falls is decreasing at the rate of

740

people each year while the population of Swift Creek is increasing at the rate of

1

500

people each year. Assumin; these rates continue into the future, in how many years from today will the population of Swift Creek equal twice the population of Canyon Falls?

The ratio of boys to girls in a school is

9: 11

400

pupils in the school, how many boys are there?

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80

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120

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180

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220

A small country emits

114

000

kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by

0.5 \%

per year for the next

5

years. In the first year of the agreement, the country will keep its emissions at

114

000

kilotons and the emissions will decrease

0.5 \%

in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the

5

year period, to the nearest whole number?

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A small country emits

54

000

kilotons of carbon dioxide per year. In a recent global agreement, the country agreed to cut its carbon emissions by

4 \%

per year for the next

14

years. In the first year of the agreement, the country will keep its emissions at

54

000

kilotons and the emissions will decrease

4 \%

in each successive year. How many total kilotons of carbon dioxide would the country emit over the course of the

14

year period, to the nearest whole number?

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\mathrm{X}

is a radioactive isotope such that every

75

years, its mass decreases by half. Given that the initial mass of a sample of Element X is

920

grams, how much of the element would remain after

3

years, to the nearest whole number?

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In a lab experiment,

480

bacteria are placed in a petri dish. The conditions are such that the number of bacteria is able to double every

22

hours. How many bacteria would there be after

25

hours, to the nearest whole number?

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\mathrm{X}

is a radioactive isotope such that every

12

years, its mass decreases by half. Given that the initial mass of a sample of Element

\mathrm{X}

\mathbf{2 0}

grams, how much of the element would remain after

18

years, to the nearest whole number?

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\mathrm{X}

is a radioactive isotope such that every

11

years, its mass decreases by half. Given that the initial mass of a sample of Element

X

5600

grams, how much of the element would remain after

10

years, to the nearest whole number?

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An element with a mass of

220

grams decays by

26.6 \%

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

10

grams of the element remaining?

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2015

, the most densely populated state in the United States was New Jersey, with a population of

8,957,907

1218

1

people per square mile. Which is the approximate land area of New Jersey to the nearest square mile?

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7

135

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7

354

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10

912

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12

354

Today, the population of Canyon Falls is

22

500

and the population of Swift Creek is

15

200

. The population of Canyon Falls is decreasing at the rate of

740

people each year while the population of Swift Creek is increasing at the rate of

1

500

people each year. Assuming these rates continue into the future, in how many years from today will the population of Swift Creek equal twice the population of Canyon Falls?

An element with mass

650

grams decays by

6 \%

per minute. How much of the element is remaining after

8

minutes, to the nearest

1

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The half-life of a substance is

40.2

million years. If a certain amount is only considered safe when its radioactivity has dropped to

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6.25\%

of the original level, approximately how much time must the substance be stored securely to be safe?

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(A)160.8

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(B)160.8

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(C)201

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(D)201