Lesson Worksheet: Applications of Exponential Functions Mathematics • 9th Grade

In this worksheet, we will practice solving real-world problems involving exponential functions.

Q1:

A microorganism reproduces by binary fission, where every hour each cell divides into two cells. Given that there were 15,141 cells to begin with, determine how many cells there were after 5 hours.

Q2:

A start-up company noticed that the number of those who use its product doubles every month. This month, they had 4,000 users. Assuming this trend continues, write an equation that can be used to calculate π‘ˆ(π‘š), the number of users in π‘š months’ time.

  • Aπ‘ˆ(π‘š)=4,000(3)
  • Bπ‘ˆ(π‘š)=4,000(π‘š)
  • Cπ‘ˆ(π‘š)=4,000(π‘š)
  • Dπ‘ˆ(π‘š)=4,000(2)
  • Eπ‘ˆ(π‘š)=4,000(2π‘š)

Q3:

The US Census is taken every ten years. The population of Texas was 3.05 million in 1900 and 20.9 million in 2000. By modeling the population growth as exponential, answer the following questions.

Write an exponential function in the form 𝑃(𝑑)=π‘ƒπ‘˜οŠ¦οŒ½ to model the population of Texas, in millions, 𝑑 decades after 1900. Round your value of π‘˜ to three decimal places.

  • A𝑃(𝑑)=(3.700)
  • B𝑃(𝑑)=1.212(3.050)
  • C𝑃(𝑑)=(3.050)
  • D𝑃(𝑑)=3.05(1.212)
  • E𝑃(𝑑)=(1.212)

According to the model, what was the population of Texas in 1950? Give your answer in millions to two decimal places.

  • A4.88 million
  • B3.70 million
  • C7.98 million
  • D9.85 million
  • E1.41 million

Using the value of π‘˜ from part 1, rewrite your function in the form 𝑃(𝑦)=𝑃(𝑏), where 𝑦 is the time in years after the year 1900. Round your value of 𝑏 to four decimal places.

  • A𝑃(𝑦)=1.0194(3.0500)
  • B𝑃(𝑦)=3.05(1.0194)
  • C𝑃(𝑦)=3.05(1.0194)
  • D𝑃(𝑦)=0.0194(3.0500)
  • E𝑃(𝑦)=3.05(0.0194)

Q4:

Radioactive element 𝐽 has a half-life of 1 week. If an experiment starts with 20 g of element 𝐽, the mass 𝑀, in grams, of element 𝐽 remaining after 𝑀 weeks can be found using the equation 𝑀=20ο€Ό12οˆο•. Write an equation to find the mass of element 𝐽 remaining after 𝑑 days.

  • A𝑀=2012
  • B𝑀=20ο€Ό17
  • C𝑀=20ο€Ό12
  • D𝑀=2012
  • E𝑀=20ο€Ό17

Q5:

A population of bacteria decreases as a result of a chemical treatment. The population 𝑑 hours after the treatment was applied can be modeled by the function 𝑃(𝑑), where 𝑃(𝑑)=6,000Γ—(0.4).

What was the population when the chemical was first applied?

What is the rate of population decrease?

  • A4% per hour
  • B1.4% per hour
  • C1.6% per hour
  • D6% per hour
  • E60% per hour

Q6:

The number of people visiting a museum is decreasing by 3% a year. This year, there were 50,000 visitors. Assuming the decline continues, write an equation that can be used to find 𝑉, the number of visitors there will be in 𝑑 years’ time.

  • A𝑉=50,000(0.97)
  • B𝑉=50,000(1.03)
  • C𝑉=50,000(0.03)
  • D𝑉=50,000(0.7)
  • E𝑉=50,000(3)

Q7:

The value of a used car depreciates at a rate of 14% every year. If the car was bought for $15,000 in February 2017, how much would it be worth in February 2023? Give your answer to the nearest one hundred dollars.

Q8:

If $800 is earning interest semiannually at 2% per annum, what is the amount after 𝑛 years?

  • A800(0.02)
  • B800(1.02)
  • C800(1.02)
  • D800(1.01)
  • E800(1.01)

Q9:

A fast-food chain wishes to reduce the amount of fat in its burgers. If it reduces the amount of fat at a rate of 5% every year, how long will it take to reduce the fat content by one quarter? Give your answer in years to two decimal places if necessary.

Q10:

On the first day, 42 liters of water are poured into a tank. Every day thereafter, three times as much water is poured into the tank as was poured on the previous day. On which day are 1,134 liters poured into the tank?

  • Aday 4
  • Bday 5
  • Cday 3
  • Dday 6
  • Eday 27

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