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Worksheet: Exponential Growth Model

Q1:

A scientist is considering two termite species: 𝐴 and 𝐡 . At the start of the experiment, there are 1 2 3 3 of 𝐴 and 1 6 4 0 of 𝐡 . They both increase exponentially: the smaller group 𝐴 at a daily growth rate of 1 . 3 % per day, which is higher than 𝐡 's growth rate of 0 . 4 % per day. On which day will 𝐴 ’s population surpass that of 𝐡 ?

  • Aday 1
  • Bday 31
  • Cday 407
  • Dday 32
  • Eday 2

What are the populations of 𝐴 and 𝐡 on the day found in the previous question? To use the model, you must round to the nearest integer.

  • A 𝐴 = 1 8 6 4 , 𝐡 = 1 8 6 3
  • B 𝐴 = 4 1 7 3 , 𝐡 = 6 2 6 0
  • C 𝐴 = 1 2 4 9 , 𝐡 = 1 2 3 8
  • D 𝐴 = 1 8 4 0 , 𝐡 = 1 3 9 5
  • E 𝐴 = 1 2 4 0 , 𝐡 = 1 2 4 3

Q2:

A man deposited 3 049 LE in a bank account with an interest rate of 1 0 % per year. Determine how much money was in the account 7 years later, given that the interest was compounded every 4 months. Give your answer correct to two decimal places.

Q3:

A man deposited 8 694 LE in a bank account with an interest rate of 6 % per year. Determine how much money was in the account 10 years later, given that the interest was compounded annually. Give your answer correct to two decimal places.

Q4:

In 1859, Thomas Austin imported 24 wild rabbits from England and released them into the wild of southern Australia to be hunted for sport.

Consider that female rabbits only breed during the year following their birth and that the rabbit population is equally shared between male and female rabbits. With a birth rate of roughly 20 rabbits per female per year, by what factor would the whole rabbit population increase per year?

What was the rabbit population after 5 years?

By what percentage did the rabbit population increase per month?

  • A50%
  • B15%
  • C 2 1 %
  • D18%
  • E3%

How many months did it take the rabbit population to reach past one thousand?

Q5:

Let the population of a city be π‘₯ . If the population increases by 1 3 % each year, what will the population of the city be in nine years’ time?

  • A l o g ( π‘₯ + 0 . 1 3 )
  • B 1 . 1 7 π‘₯
  • C 0 . 2 8 6 π‘₯
  • D 3 . 0 0 4 π‘₯
  • E l o g 9 ( π‘₯ + 0 . 1 3 )

Q6:

Chloe wants to invest some money. She would like the value of her investment to double in 10 years. Write an equation that can be used to find π‘Ÿ , the annual rate of interest required. Assume interest is compounded annually.

  • A ο€» π‘Ÿ 1 0 0  = 2 1 0
  • B ( 1 + π‘Ÿ ) = 2 1 0
  • C ( 1 + π‘Ÿ ) = 1 2 1 0
  • D ο€» 1 + π‘Ÿ 1 0 0  = 2 1 0
  • E ο€» 1 + π‘Ÿ 1 0 0  = 1 2 1 0

Q7:

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.

Q8:

The population of Malawi, in millions, is modeled by the exponential function 𝑃 ( 𝑑 ) = 3 . 6 2 ο€Ή 1 . 0 2 9   , 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 21 years
  • B 27 years and 2 months
  • C 26 years
  • D 24 years and 3 months
  • E 21 years and 4 months

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 4 . 6 5 ο€Ή 2  
  • B 𝑃 ( 𝑑 ) = 1 1 . 3 6 ο€Ή 2  
  • C 𝑃 ( 𝑑 ) = 1 1 . 3 6 ο€½ 2       
  • D 𝑃 ( 𝑑 ) = ο€Ή 2   
  • E 𝑃 ( 𝑑 ) = 1 1 . 3 6 ο€½ 2    οŽ₯   

Q9:

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

Q10:

A mathematical model predicts that the population of a country, 𝑦 million, will be given by the formula 𝑦 = 1 7 . 1 ( 1 . 0 2 ) π‘₯ , where π‘₯ is the number of years since 2015. Use this model to predict the population of the country, to the nearest million, in both 2021 and 2022.

  • A19 million, 21 million
  • B18 million, 20 million
  • C18 million, 21 million
  • D19 million, 20 million
  • E18 million, 19 million