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Lesson: Exponential Growth Model

Worksheet • 10 Questions

Q1:

A man invested 200 000 LE in a project. Each year his investment grows by 9 % . Determine the value of his investment after 7 years, giving your answer correct to two decimal places.

Q2:

The population of Malawi, in millions, is modeled by the exponential function 𝑃 ( 𝑑 ) = 3 . 6 2 ο€Ή 1 . 0 2 9  𝑑 , where 𝑑 is the time in years since January 1 1960.

To the nearest month, how long does it take for the population to double?

  • A 24 years and 3 months
  • B 21 years and 4 months
  • C 27 years and 2 months
  • D 26 years
  • E 21 years

Which year will be the first to start with a population of more than 20 million?

Find the function which represents the same exponential model, but with the input 𝑑 now being the time in years since January 1 2000. Express this function using a base of 2 rather than the previously used 1.029.

  • A 𝑃 ( 𝑑 ) = 1 1 . 3 6 ο€½ 2  𝑑 2 4 . 2 5
  • B 𝑃 ( 𝑑 ) = 1 4 . 6 5 ο€Ή 2  𝑑
  • C 𝑃 ( 𝑑 ) = 1 1 . 3 6 ο€Ή 2  𝑑
  • D 𝑃 ( 𝑑 ) = 1 1 . 3 6 ο€½ 2  𝑑 3 6 . 8 0
  • E 𝑃 ( 𝑑 ) = ο€Ή 2  2 𝑑

Q3:

A population of fruit flies quadruples every three days. Today, there were 150 fruit flies in the population under investigation.

Assuming the population continues to grow at the same rate, write an equation that can be used to find 𝐹 , the number of fruit flies expected to be in the population in 𝑑 days’ time.

  • A 𝐹 = 1 5 0 ( 4 ) 𝑑 3
  • B 𝐹 = 1 5 0 ( 3 ) 𝑑 3
  • C 𝐹 = 1 5 0 ( 4 ) 3 𝑑
  • D 𝐹 = 1 5 0 ( 3 ) 𝑑 4
  • E 𝐹 = 1 5 0 ( 3 ) 4 𝑑
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