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Worksheet: Solving Real-world Problems on Exponential Growth and Decay

Q1:

The number of bacteria in a laboratory quadruples every hour. There were initially 200 bacteria. Write an expression for , the number of bacteria hours after the initial measurement.

  • A
  • B
  • C
  • D
  • E

Q2:

The production of a gold mine is decreasing with a rate of annually. Given that the mine’s production was 6 400 kg in the first year, determine its production in the sixth year, giving your answer the nearest integer.

Q3:

A doctor injected a patient with 13 milligrams of radioactive dye that decays exponentially. After 12 minutes, there were 4.75 milligrams of dye remaining in the patient’s system. Which of the following is an appropriate model for this situation?

  • A
  • B
  • C
  • D

Q4:

The amount of money in an account doubles every 9 years. If is deposited into the account, how much will be in the account after 27 years?

Q5:

A scientist begins with 100 mg of a radioactive substance that decays exponentially. After 35 hours, 50 mg of the substance remains. How many milligrams will remain after 54 hours? If necessary, round your answer to 2 decimal places.

Q6:

The value of a car depreciates by per year. A new car costs . Write an expression for the car’s value in dollars when it is years old.

  • A
  • B
  • C
  • D
  • E

Q7:

Determine whether the data shown exhibits growth or decay, stating whether it is linear or exponential.

0 1 2 3
990 330 110
  • Alinear growth
  • Bexponential growth
  • Clinear decay
  • Dexponential decay

Q8:

The Asian elephant population years after the year 1900 is given by .

What was the Asian elephant population in 1900?

  • A
  • B
  • C
  • D
  • E

According to this model, by what percentage has the Asian elephant population decreased over a century?

  • A
  • B
  • C
  • D
  • E

Q9:

An apple loses 50% of its water content after 30 days due to dehydration. If an apple weighed 100 g when it was picked, and 84 g 10 days later, after roughly how many days will the apple weigh 50 g?

  • A55 days
  • B35 days
  • C42 days
  • D45 days
  • E40 days

Q10:

We consider that computers lose of their value every year.

Write a corresponding formula for the value of a computer years after its purchase. Let be its purchase value.

  • A
  • B
  • C
  • D
  • E

Rewrite the expression for the value of a computer years after its purchase in the form .

  • A
  • B
  • C
  • D
  • E

Deduce from your previous answer the percentage of the monthly depreciation of computers.

Q11:

A mathematical model predicts that the population of a city, million, will be given by the formula , where is the number of years from now. What does the model predict the population will be in 2 years’ time?

Q12:

The population of a city is increasing by annually. Given that the current population is 1.7 million, and assuming that the growth rate remains constant, find the population of the city in 8 years time. Give your answer in units of millions correct to two decimal places.

Q13:

At the end of 2000, the population of a country was 22.4 million. Since then, the population has increased by every year. What is the population, rounded to the nearest tenth, of the country at the end of 2037?

Q14:

Moore’s law was named after Gordon Moore who observed in the sixties that, owing to miniaturization, the number of transistors in a dense integrated circuit doubles approximately every two years. He predicted that this will last for at least one decade.

Using Moore’s law, find an explicit formula for the number of transistors in a single circuit in a year . Assume that in 1971, a circuit had transistors.

  • A
  • B
  • C
  • D
  • E

In 2011, 2.6 billion transistors were used to make a single integrated circuit (a 10-core Xeon Westmere-EX processor). Would you consider that Moore’s law was still valid in 2011?

  • Ayes
  • Bno

In 2017, 9.7 billion transistors were used to make a single integrated circuit at IBM and 19.2 billion transistors for a 32-core AMD Epyc processor. Which of these figures can be considered to fit with Moore’s law?

Q15:

The number of Ebola infections in West Africa at the start of an epidemic followed an exponential growth. It is given by , with the number of days after the first infection.

What does the coefficient 0.075 represent?

  • AIt is the time it takes for the number of infections to be multiplied by .
  • BIt is the number of new infections per day.
  • CIt is the percentage of the daily growth in the number of infections ( ).
  • D is the time it takes for the number of infections to be multiplied by .
  • EIt is the number of days after the first infection.

By rewriting the formula in the form , find the percentage of the daily growth in the number of infections. Give your answer to one decimal place.

  • A
  • B
  • C
  • D
  • E

Q16:

A savings account has no accumulated interest, but it receives a deposit of $550 every month. Can this be represented by a linear or an exponential growth model?

  • Aa linear growth model
  • Ban exponential growth model

Q17:

The temperature decreases by every 2 hours from 6 pm to 5 am. Can this be represented by a linear or an exponential decay model?

  • Aa linear decay model
  • Ban exponential decay model