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Worksheet: Introduction to Exponential Decay

Q1:

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.

Q2:

A car was valued at $ 3 8 0 0 0 in the year 2007. By 2013, the value had depreciated to $ 1 1 0 0 0 . Assuming continuous depreciation at the same rate, find, to the nearest dollar, the value of the car in 2017.

Q3:

The Asian elephant population 𝑑 years after the year 1900 is given by 𝑃 = 1 0 0 0 0 0 β‹… 0 . 2 5 𝑑 / 1 0 0 .

What was the Asian elephant population in 1900?

  • A 5 0 0 0 0
  • B 2 5 0 0 0
  • C 2 0 0 0 0 0
  • D 1 0 0 0 0 0
  • E 1 5 0 0 0

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

  • A 7 5 %
  • B 1 5 %
  • C 5 0 %
  • D 2 5 %
  • E 5 5 %

Q4:

The function 𝑦 = 𝐴 𝑏 π‘₯ represents a 1 5 % decay in each period that π‘₯ measures. What is the value of 𝑏 ?

Q5:

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

π‘₯ βˆ’ 2 βˆ’ 1 0 1 2 3
𝑦 2 4 0 0 1 2 0 0 600 300 150 75
  • Alinear growth
  • Bexponential growth
  • Clinear decay
  • Dexponential decay

Q6:

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

π‘₯ 0 1 2 3
𝑦 2 9 7 0 990 330 110
  • Alinear growth
  • Bexponential growth
  • Clinear decay
  • Dexponential decay

Q7:

Which of the functions below represents exponential decay?

  • A 𝑓 ( π‘₯ ) = 7 π‘₯
  • B 𝑓 ( π‘₯ ) = ο€Ό 1 3 8  βˆ’ π‘₯
  • C 𝑓 ( π‘₯ ) = 6 8 π‘₯
  • D 𝑓 ( π‘₯ ) = ο€Ό 1 0 3 3  π‘₯

Q8:

Which of the functions below represents exponential decay?

  • A 𝑓 ( π‘₯ ) = 6 5 π‘₯
  • B 𝑓 ( π‘₯ ) = ο€Ό 1 2 1  βˆ’ π‘₯
  • C 𝑓 ( π‘₯ ) = 1 6 π‘₯
  • D 𝑓 ( π‘₯ ) = ο€Ό 4 5 1  π‘₯

Q9:

Which of the functions below represents exponential decay?

  • A 𝑓 ( π‘₯ ) = 5 4 π‘₯
  • B 𝑓 ( π‘₯ ) = ο€Ό 1 4 8  βˆ’ π‘₯
  • C 𝑓 ( π‘₯ ) = 6 5 π‘₯
  • D 𝑓 ( π‘₯ ) = ο€Ό 2 3 2 9  π‘₯

Q10:

The value of a car depreciates by 8 % per year. A new car costs $ 2 0 0 0 0 . Write an expression for the car’s value in dollars when it is 𝑑 years old.

  • A ( 2 0 0 0 Γ— 0 . 9 2 ) 𝑑
  • B 2 0 0 0 0 + ( 0 . 9 2 ) 𝑑
  • C 2 0 0 0 0 Γ— ( 0 . 0 8 ) 𝑑
  • D 2 0 0 0 0 Γ— ( 0 . 9 2 ) 𝑑
  • E ( 2 0 0 0 Γ— 0 . 0 8 ) 𝑑