Worksheet: Exponential Decay

In this worksheet, we will practice identifying the graph of exponential decay and solving real-world problems including exponential decay.

Q1:

The population of a small town decreases by 1 1 0 every year. Today, the population is 5 0 0 0 . Write an expression for the population of the town in ๐‘ก years.

(Hint: by what do you multiply to produce a decrease of 1 1 0 ?)

  • A 5 0 0 0 + ( 0 . 9 ) ๐‘ก
  • B 5 0 0 0 ร— 0 . 9 ร— ๐‘ก
  • C ( 5 0 0 0 ร— 0 . 9 ) ๐‘ก
  • D 5 0 0 0 ร— ( 0 . 9 ) ๐‘ก
  • E 5 0 0 0 ร— ( 0 . 1 ) ๐‘ก

Q2:

Which graph demonstrates exponential decay?

  • A
  • B
  • C
  • D

Q3:

Adel and Ramy want to sell their property. The property market is going down in their city and the expected propertiesโ€™ value after ๐‘š months is given by the expression ๐‘ƒ = ๐‘ƒ โ‹… 0 . 9 5 0 ๐‘š . What is the percentage reduction in the property value per month?

  • A 9 0 %
  • B 9 5 %
  • C 9 0 . 5 %
  • D 5 %
  • E 9 . 5 %

Q4:

Engy bought a new car for three years ago. If we assume that cars lose of their value every year, how much is her car worth now, giving your answer to the nearest dollar?

Q5:

A childโ€™s ball loses 1 5 % 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.

  • A 5 cm
  • B 84 cm
  • C 27 cm
  • D 45 cm
  • E 22 cm

Q6:

The value of shares in a failing company is falling by one quarter every week. Todayโ€™s value of an investment in the company is $ 9 5 0 0 . Write an equation that can be used to find ๐ผ , the value of the investment in dollars in ๐‘ก daysโ€™ time.

  • A ๐ผ = 9 5 0 0 ๏€ผ 1 4 ๏ˆ ๐‘ก 7
  • B ๐ผ = 9 5 0 0 ๏€ผ ๐‘ก 7 ๏ˆ 3 4
  • C ๐ผ = 9 5 0 0 ๏€ผ 5 4 ๏ˆ ๐‘ก 7
  • D ๐ผ = 9 5 0 0 ๏€ผ 3 4 ๏ˆ ๐‘ก 7
  • E ๐ผ = 9 5 0 0 ๏€ผ ๐‘ก 7 ๏ˆ 1 4

Q7:

A poor-performing fund loses value at an annual rate of 2 . 3 % . Unfortunately, one of the conditions of the fund is that investments cannot be withdrawn before a minimum of 10 years without incurring a large penalty.

If $ 1 5 0 0 0 was invested, what would its value after the minimum term be? Give your answer to the nearest dollar.

  • A $ 1 2 5 0 3
  • B $ 1 1 5 5 0
  • C $ 1 3 2 0 1
  • D $ 1 1 8 8 6
  • E $ 9 5 1 0

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