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Worksheet: Introduction to Exponential Growth

Q1:

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

Q2:

A savings account offers an annual interest rate of 0 . 8 5 % . Can this be represented by a linear or an exponential growth model?

  • Aan exponential growth model
  • Ba linear growth model

Q3:

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

π‘₯ 0 1 2 3
𝑦 2 5 12.5 31.25
  • Aexponential decay
  • Blinear growth
  • Clinear decay
  • Dexponential growth

Q4:

The given table shows a video’s daily view count. How would you describe the figure’s growth?

Day 1 2 3 4 5
View Count 6 19 57 168 499
  • Alinear growth
  • Bexponential decay
  • Clinear decay
  • Dexponential growth

Q5:

Is the exponential function 𝑦 = 4 ( 1 . 2 1 ) π‘₯ growing or decaying?

  • Agrowing
  • Bdecaying

Q6:

Which of the functions below represents exponential growth?

  • A 𝑓 ( π‘₯ ) = ο€Ό 1 2  π‘₯
  • B 𝑓 ( π‘₯ ) = 2 βˆ’ π‘₯
  • C 𝑓 ( π‘₯ ) = ο€Ό 2 2 7  π‘₯
  • D 𝑓 ( π‘₯ ) = 7 9 π‘₯

Q7:

Which of the functions below represents exponential growth?

  • A 𝑓 ( π‘₯ ) = ο€Ό 1 1 6  π‘₯
  • B 𝑓 ( π‘₯ ) = 4 βˆ’ π‘₯
  • C 𝑓 ( π‘₯ ) = ο€Ό 8 1 3  π‘₯
  • D 𝑓 ( π‘₯ ) = 1 0 π‘₯

Q8:

Property rental prices downtown are increasing at a rate of 5 % per year. This year, an apartment is available for $800 a month. Write an expression for 𝑉 ( 𝑑 ) , the value in dollars of the apartment 𝑑 years from now.

  • A 𝑉 ( 𝑑 ) = ( 8 0 0 Γ— 1 . 0 5 ) 𝑑
  • B 𝑉 ( 𝑑 ) = 8 0 0 + 1 . 0 5 𝑑
  • C 𝑉 ( 𝑑 ) = 8 0 0 Γ— 1 . 0 5 𝑑
  • D 𝑉 ( 𝑑 ) = 8 0 0 Γ— 1 . 0 5 𝑑
  • E 𝑉 ( 𝑑 ) = 8 0 0 Γ— 1 . 0 5 Γ— 𝑑

Q9:

The population of a city is increasing by 3 . 1 % 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.

Q10:

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

  • A 2 0 0 + 4 𝑑
  • B 2 0 0 Γ— 4 Γ— 𝑑
  • C 2 0 0 + 4 Γ— 𝑑
  • D 2 0 0 Γ— 4 𝑑
  • E 2 0 0 Γ— 4 𝑑

Q11:

David wants to sell his apartment. He knows that, in his town, property prices have doubled in the 20 years since he bought his apartment.

Assuming that the property prices increased at a steady rate, what was the annual rate of increase? Give your answer as a percentage correct to one decimal place if necessary.

  • A
  • B
  • C
  • D
  • E

Q12:

The number of bacteria in an experiment doubles every 9 hours. Use the table to determine how many bacteria there will be after 81 hours.

Hours 9 18 27 36 45
Number of Bacteria 6 12 24 48 96