Lesson Worksheet: Exponential Growth and Decay Mathematics • 9th Grade

In this worksheet, we will practice setting up and solving exponential growth and decay equations and interpreting their solutions.

Q1:

Is the exponential function ๐‘ฆ=4(1.21)๏— growing or decaying?

  • Adecaying
  • Bgrowing

Q2:

A population of bacteria in a petri dish ๐‘ก hours after the culture has started is given by ๐‘ƒ=2,400โ‹…๐‘’๏Šฆ๏Ž–๏Šฆ๏Šฎ๏Šช๏. Amelia says this means that the growth rate is 8.4% per hour. Her friend Elizabeth, however, says that the hourly growth rate is 8.76%. Who is right?

  • AElizabeth
  • BAmelia

Q3:

A population that grows over time ๐‘ก to a fixed positive limit may be modeled by a transformed exponential function ๐‘ƒ(๐‘ก)=๐‘+๐‘Ž๐‘’๏Œป๏ for suitable ๐‘Ž, ๐‘, and ๐‘. The following is a graph of this.

If the initial and limiting populations are ๐ด and ๐ฟ, respectively, which would be a suitable function?

  • A๐ฟ+(๐ฟ+๐ด)๐‘’(๏Šซ๏)
  • B๐ฟโˆ’(๐ฟโˆ’๐ด)๐‘’(๏Šซ๏)
  • C๐ฟ+(๐ฟโˆ’๐ด)๐‘’(๏Šฑ๏Šซ๏)
  • D๐ฟโˆ’(๐ฟโˆ’๐ด)๐‘’(๏Šฑ๏Šซ๏)
  • E๐ฟโˆ’(๐ฟ+๐ด)๐‘’(๏Šฑ๏Šซ๏)

Q4:

Ethan has 73 rabbits. He believes that he will have ๐‘ง=73(4.21)๏‘ƒ๏Žข rabbits after ๐‘› months. How many rabbits does he expect to have 2 months from now?

Q5:

The given figure shows the concentration ๐‘, in micrograms per liter, of a certain drug in human blood plasma measured at different times. Considering that the concentration after โ„Ž hours can be modeled with the function ๐‘=18โ‹…0.75๏‚, by what percentage does the drugโ€™s concentration decrease every hour?

Q6:

A childโ€™s ball loses 15% of its energy every time it rebounds. By considering that the ballโ€™s kinetic energy is proportional to the height from which it was dropped, determine the height, to the nearest centimeter, that the ball must be dropped from so that it rebounds to 20 cm on the fifth bounce.

Q7:

The Asian elephant population ๐‘ก years after the year 1900 is given by ๐‘ƒ=100,000โ‹…0.25๏‘‰๏Ž ๏ŽŸ๏ŽŸ.

What was the Asian elephant population in 1900?

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

Q8:

A carโ€™s value depreciates by ๐‘Ÿ% every year. A new car costs ๐‘ƒdollars.

Write a function that can be used to calculate ๐‘‰, the carโ€™s value in dollars, after ๐‘ก years.

  • A๐‘‰(๐‘ก)=๐‘ƒ๏€ป1โˆ’๐‘Ÿ100๏‡๏
  • B๐‘‰(๐‘ก)=๏€ป๐‘ƒโˆ’๐‘Ÿ100๏‡๏
  • C๐‘‰(๐‘ก)=๐‘ƒ๏€ป๐‘Ÿ100๏‡๏
  • D๐‘‰(๐‘ก)=๐‘ƒ๏€ป1+๐‘Ÿ100๏‡๏
  • E๐‘‰(๐‘ก)=๏€ป1โˆ’๐‘Ÿ100๏‡๏

What is the value of ๐‘Ÿ for which the carโ€™s value will be halved in 3 years? Give your answer to the nearest whole number.

Q9:

The number of bacteria in a laboratory quadruples every hour. There were initially 200 bacteria. Write an expression for ๐ต(๐‘ก), the number of bacteria ๐‘ก hours after the initial measurement.

  • A200+4ร—๐‘ก
  • B200ร—4๏
  • C200+4๏
  • D200ร—4ร—๐‘ก
  • E200ร—4๏

Q10:

A cereal manufacturer decides to make their products healthier by reducing the amount of sugar in them. Their target is to reduce the amount of sugar in their product range by 20%. They plan to achieve their target in 4 years.

Write an equation they could use to find ๐‘Ÿ, the annual sugar reduction rate required to achieve their target.

  • A๏€ผ100โˆ’๐‘Ÿ100๏ˆ=0.8๏Šช
  • B(1โˆ’๐‘Ÿ)=0.8๏Šช
  • C๏€ป๐‘Ÿ100๏‡=0.8๏Šช
  • D๏€ป1โˆ’๐‘Ÿ100๏‡=0.2๏Šช
  • E(1โˆ’๐‘Ÿ)=0.2๏Šช

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